Control and calibration solutions and methods for their use

ABSTRACT

Control and calibration solutions are described that provide control and calibration data that is recognized by a test meter allowing the meter to segregate the control and calibration data from regular test data. Recognition and segregation of the control and calibration data can occur automatically with no additional input from the meter&#39;s user. Methods for use of the solutions are also provided.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No. 60/480,298, filed Jun. 20, 2003, the contents of which are hereby incorporated by reference herein.

TECHNICAL FIELD

The disclosed embodiments relate to control and calibration solutions and methods for confirming the proper operation and accuracy of a device for determining the concentration of an analyte in a fluid. The disclosed embodiments relate more particularly, but not exclusively, to the solutions and their use in conjunction with devices which may be used for measuring the concentration of glucose in blood. The solutions according to the present disclosure provide control and/or calibration data indicative of the device's performance and accuracy that is recognizable by the device. As a result, a device having appropriate instructions is able to automatically segregate the control and calibration data from normal test data and avoid their co-mingling.

BACKGROUND

Measuring the concentration of substances, particularly in the presence of other, confounding substances, is important in many fields, and especially in medical diagnosis. For example, the measurement of glucose in body fluids, such as blood, is crucial to the effective treatment of diabetes. Proper performance and calibration of the device used in the measurement and the ability to avoid the co-mingling of control and calibration data with test data is critical to providing an effective treatment.

Diabetic therapy typically involves two types of insulin treatment: basal, and meal-time. Basal insulin refers to continuous, e.g. time-released insulin, often taken before bed. Meal-time insulin treatment provides additional doses of faster acting insulin to regulate fluctuations in blood glucose caused by a variety of factors, including the metabolization of sugars and carbohydrates. Proper regulation of blood glucose fluctuations requires accurate measurement of the concentration of glucose in the blood. Failure to do so can produce extreme complications, including blindness and loss of circulation in the extremities, which can ultimately deprive the diabetic of use of his or her fingers, hands, feet, etc.

Multiple methods are known for measuring the concentration of analytes in a blood sample, such as, for example, glucose. Such methods typically fall into one of two categories: optical methods and electrochemical methods. Optical methods generally involve reflectance or absorbance spectroscopy to observe the spectrum shift in a reagent. Such shifts are caused by a chemical reaction that produces a color change indicative of the concentration of the analyte. Electrochemical methods generally involve, alternatively, amperometric or coulometric responses indicative of the concentration of the analyte. See, for example, U.S. Pat. No. 4,233,029 to Columbus, U.S. Pat. No. 4,225,410 to Pace, U.S. Pat. No. 4,323,536 to Columbus, U.S. Pat. No. 4,008,448 to Muggli, U.S. Pat. No. 4,654,197 to Lilja et al., U.S. Pat. No. 5,108,564 to Szuminsky et al., U.S. Pat. No. 5,120,420 to Nankai et al., U.S. Pat. No. 5,128,015 to Szuminsky et al., U.S. Pat. No. 5,243,516 to White, U.S. Pat. No. 5,437,999 to Diebold et al., U.S. Pat. No. 5,288,636 to Pollmann et al., U.S. Pat. No. 5,628,890 to Carter et al., U.S. Pat. No. 5,682,884 to Hill et al., U.S. Pat. No. 5,727,548 to Hill et al., U.S. Pat. No. 5,997,817 to Crismore et al., U.S. Pat. No. 6,004,441 to Fujiwara et al., U.S. Pat. No. 4,919,770 to Priedel, et al., and U.S. Pat. No. 6,054,039 to Shieh, which are hereby incorporated in their entireties.

An important limitation of electrochemical methods of measuring the concentration of a chemical in blood is the effect of confounding variables on the diffusion of analyte and the various active ingredients of the reagent. For example, the geometry and state of the blood sample must correspond closely to that upon which the signal-to-concentration mapping function is based.

The geometry of the blood sample is typically controlled by a sample-receiving portion of the testing apparatus. In the case of blood glucose meters, for example, the blood sample is typically placed onto a disposable test strip that plugs into the meter. The test strip may have a sample chamber (capillary fill space) to define the geometry of the sample. Alternatively, the effects of sample geometry may be limited by assuring an effectively infinite sample size. For example, the electrodes used for measuring the analyte may be spaced closely enough so that a drop of blood on the test strip extends substantially beyond the electrodes in all directions. Ensuring adequate coverage of the measurement electrodes by the sample, however, is an important factor in achieving accurate test results. This has proven to be problematic in the past, particularly with the use of capillary fill spaces.

Other examples of limitations to the accuracy of blood glucose measurements include variations in blood composition or state (other than the aspect being measured). For example, variations in hematocrit (concentration of red blood cells), or in the concentration of other chemicals in the blood, can effect the signal generation of a blood sample. Variations in the temperature of blood samples are yet another example of a confounding variable in measuring blood chemistry.

Finally, the accuracy of blood glucose measurements also depends on the proper performance of the test meter and its proper calibration. Thus, control and calibration reagents are needed as well as methods for their use to monitor the meter's performance and accuracy. Because the review of test data obtained over a period of time and typically stored in the meter can provide valuable trends to an individual or the individual's physician, it is important that any control or calibration data (“control/calibration data”) generated by the meter not be intermingled with test data. It is one object of the present disclosure to provide control and calibration reagents and methods for their use that will allow control and calibration data to be determined, recognized as control and calibration data by a test meter, stored in the meter, if desired, and not co-mingled with an individual's test data.

SUMMARY

In one embodiment of the present disclosure, a composition is provided for use as either a control or calibration solution (“control/calibration solution”) for a device designed to analyze a biological fluid. The composition comprises water and sufficient amounts of ionic and organic modulators to cause the solution to provide at least one response characteristic of the biological fluid and at least one response uncharacteristic of the biological fluid. With proper programming a device can detect an uncharacteristic response, recognize that a control/calibration sample is being tested and properly segregate the control/calibration data generated from regular test data.

In another embodiment of the present disclosure, a method is provided for identifying control/calibration data generated by a medical device. The method comprises: (a) selecting a control/calibration solution containing a sufficient amount of a modulator to cause the solution to provide a characteristic response and an uncharacteristic response to an applied signal; (b) applying a signal to the control/calibration solution; (c) measuring the characteristic response and the uncharacteristic response; (d) using the characteristic response to provide control/calibration data; and (e) using the uncharacteristic response to identify control/calibration data.

In another embodiment of the present disclosure, a method is provided for identifying control/calibration data generated by a device having a test chamber and designed to analyze a biological fluid. The method comprises (a) selecting a control/calibration solution containing ionic and organic modulators in relative amounts sufficient to cause the solution to provide a characteristic response and an uncharacteristic response; (b) introducing the solution into the test chamber; (c) applying a signal to the solution; (d) generating and measuring an uncharacteristic response; and (e) using the uncharacteristic response to identify control/calibration data.

In another embodiment of the present disclosure, a method is provided for generating and identifying control/calibration data generated by a device designed to analyze a biological fluid. The method comprises: (a) providing a biological fluid test strip; (b) providing a control/calibration solution containing a known concentration of analyte and ionic and organic modulators in relative amounts sufficient to cause the solution to provide a characteristic response and an uncharacteristic response; (c) applying the solution to the test strip; (d) applying test and control/calibration signals to the solution; (e) measuring a first response to the test signal; (f) using the first response to determine the analyte concentration; (g) measuring a second response to the control/calibration signal; and (h) using the second response to identify the analyte concentration as control/calibration data. A solution having no measurable amount of analyte has a known zero concentration of the analyte.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be further described, by way of example only, with reference to the accompanying drawings, in which:

FIG. 1 is a diagram of a first embodiment excitation signal suitable for use in a system and method according to the present disclosure, having a serially-applied AC component and DC component.

FIG. 2 is a diagram of a second embodiment excitation signal suitable for use in a system and method according to the present disclosure, having a simultaneously-applied AC component and DC component.

FIGS. 3A-B illustrate a first embodiment test strip of the present disclosure.

FIG. 4 is a diagram of an excitation signal utilized in the test of Example 1.

FIG. 5 is a plot of the correlation coefficient r² (glucose vs. DC current) versus Read Time for the test of Example 1 with no incubation time.

FIG. 6 is a plot of the correlation coefficient r² (glucose vs. DC current) versus Read Time for the test of Example 1 with varying incubation time.

FIG. 7 is a plot of AC admittance versus hematocrit for the test of Example 2.

FIG. 8 is a plot of uncompensated DC current versus glucose for the test of Example 2.

FIG. 9 is a plot of the predicted glucose response versus the actual glucose response for the test of Example 2.

FIG. 10 is a diagram of an excitation signal utilized in the test of Example 3.

FIG. 11 is a plot of the AC phase angle versus reference glucose for the test of Example 3.

FIG. 12 is a plot of the predicted glucose response versus the actual glucose response for the test of Example 3.

FIG. 13 is a diagram of an excitation signal utilized in the test of Example 4.

FIG. 14 is a plot of AC admittance versus hematocrit (parametrically displayed with temperature) for the test of Example 4.

FIG. 15 is a plot of the uncompensated DC response versus actual glucose for the test of Example 4.

FIG. 16 is a plot of the predicted glucose response versus actual glucose response for the test of Example 4.

FIGS. 17A-B illustrate a second embodiment test strip of the present disclosure.

FIG. 18 is a plot parametrically illustrating the correlation coefficient r² between the DC current response and glucose level as Read Time varies for three combinations of temperature and hematocrit in the test of Example 5.

FIG. 19 is a diagram of the excitation signal utilized in the test of Example 5.

FIG. 20 is a plot of AC admittance versus hematocrit as temperature is parametrically varied in the test of Example 5.

FIG. 21 is a plot of AC admittance phase angle versus hematocrit as temperature is parametrically varied in the test of Example 5.

FIG. 22 is a plot of the uncompensated DC response versus actual glucose for the test of Example 5.

FIG. 23 is a plot of the predicted glucose response versus actual glucose response for the test of Example 5.

FIG. 24 is a diagram of the excitation signal utilized in the test of Example 6.

FIG. 25 is a plot of the correlation coefficient r² between hematocrit and DC response current plotted against hematocrit in the test of Example 6.

FIG. 26 is a plot of AC admittance phase angle versus hematocrit for the test of Example 6.

FIG. 27 is a plot of the uncompensated DC response versus actual glucose for the test of Example 6.

FIG. 28 is a plot of the compensated DC response versus actual glucose for a 1.1 second Total Test Time of Example 6.

FIG. 29 is a plot of the compensated DC response versus actual glucose for a 1.5 second Total Test Time of Example 6.

FIG. 30 is a plot of the compensated DC response versus actual glucose for a 1.9 second Total Test Time of Example 6.

FIG. 31 is a table detailing the heights and widths of the capillary fill channels used in the test devices of Example 8, as well as schematic diagrams of convex and concave sample flow fronts in a capillary fill space.

FIGS. 32A-C are schematic plan views of a test strip illustrating the potential for biased measurement results when a concave flow front encounters a prior art dose sufficiency electrode.

FIG. 33 is a schematic plan view of a test strip of the present disclosure having a pair of perpendicular dose sufficiency electrodes that are independent from the measurement electrodes.

FIGS. 34A-B are schematic plan views of the test strip of FIG. 33 containing samples with convex and concave flow fronts, respectively.

FIGS. 35A-B are schematic plan views of a test strip of the present disclosure having a pair of parallel dose sufficiency electrodes that are independent from the measurement electrodes.

FIG. 36 is a schematic plan view of the test strip of FIG. 35, schematically illustrating the electric field lines that communicate between the electrode gap when the electrodes are covered with sample.

FIG. 37 is a plot of AC admittance at 20 kHz versus temperature illustrating a pattern of separation between the 20 kHz admittance of blood samples and the 20 kHz admittance of control samples.

FIG. 38 is a plot of the Matrix ID function versus temperature for the test data illustrated in FIG. 37 illustrating how the Matrix ID function (Equation 22) for blood samples is consistently positive whereas the Matrix ID for control samples is consistently negative.

FIG. 39 is a plot of AC phase angle at 20 kHz versus temperature illustrating a pattern of separation between the 20 kHz phase angle of blood samples and the 20 kHz phase angle of control samples.

FIG. 40 is a plot of AC admittance at 20 kHz versus temperature illustrating a pattern of separation between the 20 kHz admittance of blood samples and the 20 kHz admittance of control samples.

FIG. 41 is a plot of the Matrix ID function versus temperature for the test data from Example 10 illustrating how the Matrix ID function (Equation 23a) for blood samples is consistently negative whereas the Matrix ID for control samples is consistently positive.

FIG. 42 is a typical plot of DC response versus time for a blood sample and a control sample.

FIG. 43 is a plot of a typical Cottrell Failsafe Ratio (“CFR”) versus temperature for a blood sample and for a control sample.

FIG. 44 is a plot of the Matrix ID function versus temperature for typical Cottrell Failsafe Ratios derived for blood and control samples illustrating how the Matrix ID function (Equation 24) is consistently positive for blood samples and consistently negative for control samples.

DETAILED DESCRIPTION

For the purposes of promoting an understanding of the principles of the invention, reference will now be made to the embodiment illustrated in the drawings, and specific language will be used to describe that embodiment. It will nevertheless be understood that no limitation of the scope of the invention is intended. Alterations and modifications in the illustrated device, and further applications of the principles of the invention as illustrated therein, as would normally occur to one skilled in the art to which the invention relates are contemplated, are desired to be protected. In particular, although embodiments of the invention are discussed in terms of a blood glucose meter, it is contemplated that the invention can be used with devices for measuring other analytes and other sample types. Such alternative embodiments require certain adaptations to the embodiments discussed herein that would be obvious to those skilled in the art.

The entire disclosure of U.S. applications entitled, SYSTEM AND METHOD FOR ANALYTE MEASUREMENT USING AC EXCITATION (Pub. No.: US 2004/0157339 A1, Pub. Date: Aug. 12, 2004), DEVICE AND METHODS RELATING TO ELECTROCHEMICAL BIOSENSORS (Pub. No.: US 2005/0023152 A1, Pub. Date: Feb. 3, 2005), and TEST STRIP WITH SLOT VENT (Pub. No.: US 2005/0013731 A1, Pub. Date: Jan. 20, 2005) are hereby incorporated by reference in their entireties.

One aspect of the present disclosure involves novel control/calibration solutions, capable of generating two responses. One response generated is characteristic of the fluid being examined (the “characteristic response) and one response generated is uncharacteristic of the fluid being examined (the “uncharacteristic response”). The uncharacteristic response can allow a measuring device to recognize that the data being generated is not test data. This can be accomplished by comparing the uncharacteristic response to a set of responses generated from test samples and on file in the device or by setting a limit for the response based on expected responses for test samples. Data associated with a response uncharacteristic of test data on file or above or below the limit set can be distinguished from test data and identified as control/calibration data by a properly programmed medical device. Once identified, control/calibration data can be segregated from regular test data generated by the device. Identifying control/calibration data includes recognizing that the data generated is not test data or recognizing that the data is not test data and affirmatively determining that because the data is not test data, that it is control/calibration data. Another aspect of the present disclosure involves methods for utilizing the novel control and calibration solutions to determine whether the device is performing properly and accurately. A control or calibration measurement can be carried out with a range of testing devices using a variety of methods to determine analyte concentration as illustrated in the discussions and examples that follow.

The systems and methods described herein permit the accurate measurement of an analyte in a fluid. In particular, the measurement of the analyte remains accurate despite the presence of interferants, which would otherwise cause error. For example, a blood glucose meter measures the concentration of blood glucose without error that is typically caused by variations in the temperature and the hematocrit level of the sample. The accurate measurement of blood glucose is invaluable to the prevention of blindness, loss of circulation, and other complications of inadequate regulation of blood glucose in diabetics. An additional advantage of a system and method described herein is that measurements can be made much more rapidly and with much smaller sample volumes, making it more convenient for the diabetic person to measure their blood glucose. Likewise, accurate and rapid measurement of other analytes in blood, urine, or other biological fluids provides for improved diagnosis and treatment of a wide range of medical conditions. Periodic use of the control and calibration solutions according to the present disclosure provides a check of the device's performance and accuracy. Because the control and calibration data produced is recognizable by the device, its segregation from test data is possible allowing the device to separately store control and calibration data and test data for later review.

It will be appreciated that electrochemical blood glucose meters typically (but not always) measure the electrochemical response of a blood sample in the presence of a reagent. The reagent reacts with the glucose to produce charge carriers that are not otherwise present in blood. Consequently, the electrochemical response of the blood in the presence of a given signal is intended to be primarily dependent upon the concentration of blood glucose. Secondarily, however, the electrochemical response of the blood to a given signal is dependent upon other factors, including hematocrit and temperature. See, for example, U.S. Pat. Nos. 5,243,516; 5,288,636; 5,352,351; 5,385,846; and 5,508,171, which discuss the confounding effects of hematocrit on the measurement of blood glucose, and which are hereby incorporated by reference in their entireties. In addition, certain other chemicals can influence the transfer of charge carriers through a blood sample, including, for example, uric acid, bilirubin, and oxygen, thereby causing error in the measurement of glucose.

One embodiment of the system and method described for measuring blood glucose operates generally by using the frequency-dependence of the contribution of various factors to the impedance (from which admittance magnitude and phase angle may be derived) of a blood sample. Because the contribution of various factors to the impedance of a blood sample is a function of the applied signal, the effects of confounding factors (that is, those other than the factors sought to be measured) can be substantially reduced by measuring the impedance of the blood sample to multiple signals. In particular, the effects of confounding factors, (primarily temperature and hematocrit, but also including chemical interferants such as oxygen), contribute primarily to the resistivity of the sample, while the glucose-dependent reaction contributes primarily to the capacitance. Thus, the effects of the confounding factors can be eliminated by measuring the impedance of the blood sample to an AC excitation, either alone or in combination with a DC excitation. The impedance (or the impedance derived admittance and phase information) of the AC signal is then used to correct the DC signal or AC derived capacitance for the effects of interferants.

It will be appreciated that measurements at sufficiently high AC frequencies are relatively insensitive to the capacitive component of the sample's impedance, while low frequency (including DC) measurements are increasingly (with decreasing frequency) sensitive to both the resistive and the capacitive components of the sample's impedance. The resistive and capacitive components of the impedance can be better isolated by measuring the impedance at a larger number of frequencies. However, the cost and complexity of the meter increases as the number of measurements increases and the number of frequencies that need to be generated increases. Thus, in one embodiment, the impedance may be measured at greater than ten frequencies, but preferably at between two and ten frequencies, and most preferably at between two and five frequencies.

As used herein, the phrase “a signal having an AC component” refers to a signal which has some alternating potential (voltage) portions. For example, the signal may be an “AC signal” having 100% alternating potential (voltage) and no DC portions; the signal may have AC and DC portions separated in time; or the signal may be AC with a DC offset (AC and DC signals superimposed).

Sample Measurement with Successive AC and DC Signals

FIG. 1 illustrates an excitation signal suitable for use in a system indicated generally at 100, in which DC excitation and four frequencies of AC excitation are used. FIG. 1 also illustrates a typical response to the excitation when the excitation is applied to a sample of whole blood mixed with an appropriate reagent, the response indicated generally at 102. A relatively high frequency signal is applied, starting at time 101. In the embodiment illustrated the frequency is between about 10 kHz and about 20 kHz, and has an amplitude between about 12.4 mV and about 56.6 mV. A frequency of 20 kHz is used in the example of FIG. 1. Those skilled in the art will appreciate that these values may be optimised to various parameters such as cell geometry and the particular cell chemistry.

At time 110 a test strip is inserted into the meter and several possible responses to the insertion of the test strip into the glucose meter are shown. It will be appreciated that the test strip may also be inserted before the excitation signal 100 is initiated (i.e. before time 101); however, the test strip itself may advantageously be tested as a control for the suitability of the strip. It is therefore desirable that the excitation signal 100 be initiated prior to test strip insertion. For example, relatively large current leakage, as shown at 112, may occur if the strip is wet, either because the test strip was pre-dosed, or due to environmental moisture. If the test strip has been pre-dosed and permitted to largely or completely dry out, an intermediate current leakage may occur, as shown at 114. Ideally, insertion of the test strip will cause no or negligible leakage current due to an expected absence of charge carriers between the test electrodes, as shown at 116. Measured current leakage above a predetermined threshold level will preferably cause an error message to be displayed and prevent the test from continuing.

Once a suitable test strip has been inserted, the user doses the strip, as shown at time 120. While the blood sample is covering the electrodes the current response will rapidly increase, as the glucose reacts with the reagent and the contact area increases to maximum. The response current will reach a stable state, which indicates the impedance of the sample at this frequency. Once this measurement is made and recorded by the test meter, the excitation frequency is then stepped down to about 10 kHz in the illustrated embodiment, as shown at time 130. Another measurement is made and recorded by the test meter, and the frequency is stepped down to about 2 kHz in the illustrated embodiment, as shown at 140. A third measurement is made and recorded by the test meter at this frequency. A fourth measurement is made at about 1 kHz in the illustrated embodiment, as shown at 150. In the illustrated embodiment, measurements are taken at regular intervals (e.g. 10 points per cycle). It will be appreciated that the stable state response may be measured as current or voltage (preferably both magnitude and phase) and the impedance and/or admittance can be calculated therefrom. Although the present specification and claims may refer alternately to the AC response as impedance or admittance (magnitude and/or phase), resistance, conductivity, current or charge, and to the DC response as current, charge, resistance or conductivity, those skilled in the art will recognize that these measures are interchangeable, it only being necessary to adjust the measurement and correction mathematics to account for which measure is being employed. In the illustrated embodiment, the test meter applies a voltage to one electrode and measures the current response at the other electrode to obtain both the AC and DC response.

In certain alternative embodiments measurements are made at fewer or more frequencies. Preferably measurements are made at least two AC frequencies at least an order of magnitude apart. If more than two AC frequencies are used, then it is preferable that the highest and lowest frequencies be at least an order of magnitude apart.

It will be appreciated that various waveforms may be used in an AC signal, including, for example, sinusoidal, trapezoidal, triangle, square and filtered square. In the presently preferred embodiment the AC signal has a filtered square waveform that approximates a sine wave. This waveform can be generated more economically than a true sine wave, using a square wave generator and one or more filters.

Once all four AC measurements are made, the signal is preferably briefly reduced to zero amplitude, as shown at 160. The DC excitation is then begun, as shown at 170. The amplitude of the DC excitation is advantageously selected based on the reagent being used, in order to maximise the resulting response or response robustness. For example, if ferricyanide is being used in a biamperometry system, the DC amplitude is preferably about 300 mV. For another example, if a nitrosoaniline derivative is being used in a biamperometry system, the DC amplitude is preferably about 500-550 mV. In the alternative, if a third reference electrode is used, the DC applitude is preferably 600 mV (versus the silver/silver chloride reference electrode) for ferricyanide, and 40-100 mV (versus the silver/silver chloride reference electrode) for nitrosoaniline derivative. During DC excitation, measurements are preferably made at a rate of 100 pts/sec. The current response will follow a decay curve (known as a Cottrell curve), as the reaction is limited by the diffusion of unreacted glucose next to the working electrode. The resulting stable-state amplitude (measured or projected) is used to determine a glucose estimation of the sample, as is known in the art. A corrected estimation is then determined that corresponds more closely to the concentration of glucose in the blood, by using the impedance of the sample to the AC signal to correct for the effects of interferants, as explained in greater detail hereinbelow.

It will be appreciated that the method illustrated may also be used to measure the concentration of other analytes and in other fluids. For example, the methods disclosed may be used to measure the concentration of a medically significant analyte in urine, saliva, spinal fluid, etc. Likewise, by appropriate selection of reagent a method according to the method illustrated may be adapted to measure the concentration of, for example, lactic acid, hydroxybutyric acid, etc.

Sample Measurement with Simultaneously Applied AC and DC Signals

It will be appreciated that at least some of the applied DC and AC components can also be applied simultaneously. FIG. 2 illustrates an excitation signal suitable for use in a system and method according to the illustrated embodiment in which some of the AC and DC components are applied simultaneously, indicated generally at 200, and having corresponding events numbered correspondingly to FIG. 1 (so, for example, the signal 200 is initiated at time 201, and a strip is inserted at time 210, etc.). As with the signal 100, the signal 200 has a frequency of about 10-20 kHz and an amplitude of about 12.4-56.6 mV. However, after the strip has been dosed, as shown at time 220, a DC offset is superimposed, as shown at 270. Typical AC and DC responses are shown in FIG. 2. The AC and DC responses are measured simultaneously and mathematically deconvoluted and used to determine the impedance (admittance magnitude and phase) and the amperometric or coulometric response.

A system for measuring blood glucose is disclosed that advantageously employs a blood glucose meter and test strips generally similar to those used in prior art systems, such as those commercially available from Roche Diagnostics, and such as are described in U.S. Pat. Nos. 6,270,637; and 5,989,917, which are hereby incorporated in their entireties. These test strips provide apparati having a sample cell in which the blood sample is received for testing, and electrodes disposed within the sample cell through which the excitation signal is provided and the measurements are made. Those skilled in the art will appreciate that these test strips and meters may advantageously be used for the measurement of glucose in blood, but that other apparati may be more suitable for the measurement of other analytes or other biological fluids when practising the methods disclosed.

A suitable glucose meter may be adapted from such known meters by the addition of electronic circuitry that generates and measures signals having AC and DC components, such as those described hereinabove, and by being programmed to correct the DC measurement using the AC measurement(s), as described in greater detail hereinbelow. It will be appreciated that the specific geometry and chemistry of the test strips can cause variations in the relationships between the concentration of glucose, hematocrit, and temperature, and the impedance of a sample. Thus, a given combination of test strip geometry and chemistry must be calibrated, and the meter programmed with the corresponding algorithm. Glucose meters of the type disclosed herein comprehend the application of excitation signals in any order and combination. For example, the present invention comprehends the application of 1) AC only, 2) AC then DC, 3) AC then DC then AC, 4) DC then AC, and 5) AC with a DC offset, just to name a few of the possible permutations.

The use of the complex AC impedance measurement data to correct for the effects of interferants on the DC measurement is advantageously illustrated by the following series of examples. More particularly, novel control and calibration solutions and methods for their use to determine the performance and accuracy of test devices are provided, wherein the data generated can be recognized by the device as control/calibration data and not co-mingled with normal test data maintained by the device. Examples 1 through 8 illustrate methods that can facilitate improvements in accuracy and test speed when measuring the concentration of an analyte in a test specimen. Although these examples deal with correcting for the interfering effects of hematocrit and temperature on blood glucose determinations, those skilled in the art will recognize that the teachings of the present methods are equally useful for correcting for the effects of other interferants in both blood glucose measurements and in the measurement of other analytes. Furthermore, the present specification refers to steps such as “determine the hematocrit value” and “determine the temperature,” etc. To use the hematocrit value as an example, it is intended that such statements include not only determining the actual hematocrit value, but also a hematocrit correction factor vs. some nominal point. In other words, the process may never actually arrive at a number equal to the hematocrit value of the sample, but instead determine that the sample's hematocrit differs from a nominal value by a certain amount. Both concepts are intended to be covered by statements such as “determine the hematocrit value.”

Examples 9-11 illustrate how the principles of the present disclosure provide control and calibration solutions and methods for their use to monitor a test meter's performance and accuracy. The control/calibration solutions according to this disclosure contain a sufficient amount of at least one modulator, which can be ionic or organic (or both), to cause the solution to provide a characteristic response and an uncharacteristic response to an applied signal. A suitable applied signal can have AC and/or DC components. An uncharacteristic response can be uncharacteristically high or uncharacteristically low (as defined by predetermined limits), allowing control and/or calibration data generated from the solutions to be readily identified. The application of a mathematical function to the generated data facilitates the test meter's ability to distinguish control and/or calibration data from normal test data without the user's input. Embodiments of this function are referred to herein as “Matrix ID.”

EXAMPLE 1 DC-Only Measurement Dose Response Study

The measurements made in Example 1 were achieved using the test strip illustrated in FIGS. 3A-B and indicated generally at 300. The test strip 300 includes a capillary fill space containing a relatively thick film reagent and working and counter electrodes, as described in U.S. Pat. No. 5,997,817, which is hereby incorporated by reference. The test strip 300 is commercially available from Roche Diagnostics Corporation (Indianapolis, Ind.) under the brand name Comfort Curve®. The ferricyanide reagent used had the composition described in Tables I and II.

TABLE I Reagent Mass Composition - Prior to Dispense and Drying Mass for Component % w/w 1 kg Solid Polyethylene oxide (300 kDa) 0.8400% 8.4000 g Solid Natrosol 250M 0.0450% 0.4500 g Solid Avicel RC-591F 0.5600% 5.6000 g Solid Monobasic potassium phosphate 1.2078% 12.0776 g (annhydrous) Solid Dibasic potassium phosphate 2.1333% 21.3327 g (annhydrous) Solid Sodium Succinate hexahydrate 0.6210% 6.2097 g Solid Quinoprotein glucose 0.1756% 1.7562 g dehydrogenase (EnzC#: 1.1.99.17) Solid PQQ 0.0013% 0.0125 g Solid Trehalose 2.0000% 20.0000 g Solid Potassium Ferricyanide 5.9080% 59.0800 g Solid Triton X-100 0.0350% 0.3500 g solvent Water 86.4731% 864.7313 g % Solids 0.1352687 Target pH 6.8 Specific Enzyme Activity Used (U/mg) 689 DCIP Dispense Volume per Sensor 4.6 mg

TABLE II Reagent Layer Composition - After Drying Mass per Component % w/w Sensor Solid Polyethylene oxide (300 kDa) 6.2099% 38.6400 ug Solid Natrosol 250M 0.3327% 2.0700 ug Solid Avicel RC-591F 4.1399% 25.7600 ug Solid Monobasic potassium phosphate 8.9286% 55.5568 ug (annhydrous) Solid Dibasic potassium phosphate 15.7706% 98.1304 ug (annhydrous) Solid Sodium Succinate hexahydrate 4.5906% 28.5646 ug Solid Quinoprotein glucose dehydrogenase 1.2983% 8.0784 ug (EnzC#: 1.1.99.17) Solid PQQ 0.0093% 0.0576 ug Solid Trehalose 14.7854% 92.0000 ug Solid Potassium Ferricyanide 43.6760% 271.7680 ug Solid Triton X-100 0.2587% 1.6100 ug

In the measurements, blood samples were applied to test strip 300 and the excitation potentials illustrated in FIG. 4 were applied to the electrodes. The excitation comprised a 2 kHz 40 mV_(rms) (56.56 mV peak) AC signal applied between 0 seconds and approximately 4.5 seconds after sample application, followed by a 300 mV DC signal applied thereafter. For the calculations of this example, however, only the DC measurement data was analyzed.

In order to determine the minimum needed DC excitation time, a “dose response” study was performed, in which glycollyzed (glucose depleted) blood was divided into discrete aliquots and controlled levels of glucose were added to obtain five different known levels of glucose in the blood samples. The resulting DC current profile was then examined as two parameters were varied. The first parameter was the Incubation Time, or the time between the detection of the blood sample being applied to the test strip 300 and the application of the DC potential to the test strip 300. The second parameter to be varied was the Read Time, or the time period after application of the DC potential and the measurement of the resulting current. The length of time between detection of the blood sample being applied to the test strip to the taking of the last measurement used in the concentration determination calculations is the Total Test Time. In this study, therefore, the sum of the Incubation Time and the Read Time is the Total Test Time. The results of this study are illustrated in FIGS. 5 and 6.

In FIG. 5, the DC response was measured with no incubation time (Read Time=Total Test Time). FIG. 5 plots the correlation coefficient r² versus Read Time. As can be seen, the correlation exceeds 0.95 within 1.0 second. In FIG. 6, the DC response was measured with varying Incubation Time. When an Incubation Time is provided (even an Incubation Time as short as two (2) seconds), the r² value rose to over 0.99 in 0.5 seconds or less after application of the DC potential.

The barrier to implementation of such fast test times in a consumer glucose test device, however, is the variation from blood sample to blood sample of the level of interference from the presence of blood cells in the sample. The hematocrit (the percentage of the volume of a blood sample which is comprised of cells versus plasma) varies from individual to individual. The interference effect of hematocrit on such measurements is fairly complex. In the tests of Example 1, however, all samples contained the same level of hematocrit. With no variable hematocrit influence at the different glucose levels, the hematocrit term cancels out in the correlation figures.

EXAMPLE 2 Combined AC and DC Measurement of Capillary Blood Samples

The measurements made in Example 2 were also achieved using the test strip illustrated in FIGS. 3A-B and indicated generally at 300. As described above, the test strip 300 includes a capillary fill space containing a relatively thick film reagent and working and counter electrodes, as described in U.S. Pat. No. 5,997,817, which is hereby incorporated herein by reference.

In the measurements, capillary blood samples from various fingerstick donors were applied to test strip 300 and the excitation potentials illustrated in FIG. 4 were applied to the electrodes. The excitation comprised a 2 kHz 40 mV_(rms) AC signal applied between 0 seconds and approximately 4.5 seconds after sample application, followed by a 300 mV DC signal applied thereafter.

In this Example 2, the AC response of the sample was derived as admittance (the inverse of impedance). The admittance response is proportionate to the hematocrit level of the sample in a temperature dependent manner. The relationship between admittance, hematocrit and testing temperature is illustrated in FIG. 7. The data used for the admittance charted in FIG. 7 is the last admittance measurement made for each sample during the AC portion of the excitation illustrated in FIG. 4.

Regression analysis of this data allows admittance, hematocrit and temperature to be related according to the following formula: H _(est) =c ₀ +c ₁ Y _(2kHz) +c ₂ dT  (Equation 1) Using this relationship to predict the blood hematocrit is accomplished using test temperature data reported by the temperature sensor in the meter and the measured admittance. In Equation 1, c₀, c₁ and c₂ are constants, dT is the deviation in temperature from a center defined as “nominal” (24° C. for example), and H_(est) is the estimated deviation in hematocrit from a similar “nominal” value. For the present purposes, the actual hematocrit value is not necessary, and it is generally preferred to produce a response which is proportionate but centers around a nominal hematocrit. Thus, for a 70% hematocrit, the deviation from a nominal value of 42% would be 28%, while conversely for a 20% hematocrit the deviation from that same nominal value would be −22%.

By using the AC admittance measurement to estimate the hematocrit level using Equation 1, the accuracy y of the DC glucose response can be greatly improved by combining the estimated hematocrit, temperature and DC response to correct for the hematocrit interference in the DC response as follows: PRED=(a ₀ +hct ₁ H _(est) +hct ₂ H _(est) ²+tau₁ dT+tau₂ dT ²)+(a ₁ DC)(1+hct ₃ H _(est) +hct ₄ H _(est) ²)(1+tau₃ dT+tau₄ dT ²)  (Equation 2) where DC is the measured glucose current response to the applied DC signal and PRED is the compensated (predicted) glucose response corrected for the effects of hematocrit and temperature. The constants (a₀, hct₁, hct₂, tau₁, tau₂, a₁, hct₃, hct₄, tau₃ and tau₄) in Equation 2 can be determined using regression analysis, as is known in the art.

FIG. 8 illustrates the uncompensated 5.5 second DC glucose response of all of the capillary blood samples as temperature varies (ignoring the AC measurement data). As will be appreciated, there is a wide variation in the DC current response as temperature and hematocrit vary. FIG. 9 illustrates the correlation between the actual blood glucose level of the sample versus the predicted response using Equation 2. As can be seen, when the DC response is compensated for hematocrit levels using the AC response data, r² values of 0.9404 to 0.9605 are achieved with a Total Test Time of 5.5 seconds.

EXAMPLE 3 Use of AC Phase Angle to Estimate Blood Glucose Levels and Hematocrit

The measurements made in Example 3 were also achieved using the test strip illustrated in FIGS. 3A-B and indicated generally at 300. As described above, the test strip 300 includes a capillary fill space containing a relatively thick film reagent and working and counter electrodes, as described in U.S. Pat. No. 5,997,817, which is hereby incorporated by reference. Because hematocrit levels from capillary blood samples typically vary only between 30%-50%, spiked venous blood samples having a hematocrit range from 20%-70% were used for this Example 3. Five levels of glucose, temperature (14, 21, 27, 36 and 42° C.) and hematocrit (20, 30, 45, 60 and 70%) were independently varied, producing a covariance study with 125 samples.

In the measurements, blood samples were applied to test strip 300 and the excitation potentials illustrated in FIG. 10 were applied to the electrodes. The excitation comprised a 2 kHz AC signal for approximately 4.1 seconds, a 1 kHz AC signal for approximately 0.1 seconds, and a 200 Hz signal for approximately 0.1 seconds. All three AC signals had an amplitude of 56.56 mV peak. No DC excitation was used in this example. The Total Test Time was 4.3 seconds from sample application time.

It was found that another component of the AC response, the phase angle (particularly at lower frequencies, such as 200 Hz in this Example 3), is also a function of the sample glucose level in the case of this test strip and reagent. This relationship is demonstrated in FIG. 11, where the AC phase angle for each of the three test frequencies is plotted versus the reference glucose level. Regression analysis for each of the three frequencies produces AC phase angle-to-reference glucose level r² correlation values of 0.9114 at 2 kHz, 0.9354 at 1 kHz, and 0.9635 at 200 Hz. The present method therefore comprehends the use of the AC phase angle to measure glucose levels. The AC excitation frequency producing the measured phase angle is preferably 2 kHz or below, more preferably 1 kHz or below, and most preferably 200 Hz or below, but not including DC excitation.

The linearized relationship between the 200 Hz phase angle response and the blood glucose level is as follows: P _(eff)=(Φ_(200 Hz)/Γ)^(−γ)  (Equation 3) where P_(eff) is the effective phase, which is proportional to glucose, the terms Γ and γ are constants, and Φ is the measured AC phase angle.

Using the same approach to compensate for temperature and hematocrit as used in Example 1 above (see Equations 1 and 2) produced a predictive algorithm as follows: PRED=(a ₀ +hct ₁ H _(est) +hct ₂ H _(est) ² +tau ₁ dT+tau₂ dT ²)+(a ₁ P _(eff))(1+hct ₃ H _(est) +hct ₄ H _(est) ²)(1+tau₃ dT+tau₄ dT ²)  (Equation 4) The resulting compensated (predicted) response PRED versus glucose for the 125 blood samples (each tested with eight test strips) is shown in FIG. 12. The r² correlation of the PRED response vs. known glucose level, where all temperatures and all hematocrits are combined, is 0.9870. This Example 3 demonstrates again the value of AC measurements for compensating for interferants that reduce the accuracy of blood glucose measurements. Using an existing commercially available sensor, the present method yields a 4.3 second Total Test Time with an overall r² of 0.9870.

It was also determined that AC phase angle measurements can produce hematocrit level measurements that are almost immune to the effects of temperature variation. In another covariant study of 125 samples (five glucose concentrations, five hematocrit concentrations and five temperatures), each of the samples was tested using an excitation profile of 20 kHz, 10 kHz, 2 kHz, 1 khz and DC. The AC phase angle at various frequencies was related to glucose, hematocrit and temperature using linear regression to determine the coefficients of the following formula at each of the four AC frequencies: Phase=c ₀ +c ₁ Glu+c ₂ HCT+c ₃Temp  (Equation 5) where Glu is the known glucose concentration, HCT is the known hematocrit concentration and Temp is the known temperature.

The determined coefficients revealed that the temperature coefficient (c₃) was essentially zero at 20 kHz and 10 kHz, cancelling temperature from the equation at these frequencies. Furthermore, the glucose coefficient (c₁) is essentially zero at all of the AC frequencies because, as explained hereinabove, the higher frequency AC impedance measurements are largely unaffected by glucose levels and are therefore useful for measuring the levels of interfering substances. It was therefore found that the hematocrit level could be determined independent of temperature and glucose level using only the AC phase angle measurements. In a preferred embodiment, the hematocrit may be measured using the phase angle data from all four measured frequencies: H _(est) =c ₀ +c ₁Φ_(20kHz) +c ₂Φ_(10kHz) +c ₃Φ_(2kHz) +c ₄Φ_(1kHz)  (Equation 6) Those skilled in the art will recognise that that the coefficients can be empirically determined for any particular test strip architecture and reagent chemistry. The methods described may be used to estimate hematocrit using only AC phase angle measurements preferably made at at least one AC frequency, more preferably made at least two AC frequencies, and most preferably made at least four AC frequencies.

EXAMPLE 4 Combined AC and DC Measurement Using Nitrosoaniline Reagent

The measurements made in Example 4 were also achieved using the test strip illustrated in FIGS. 3A-B and indicated generally at 300. As described above, the test strip 300 includes a capillary fill space containing a relatively thick film reagent and working and counter electrodes, as described in U.S. Pat. No. 5,997,817, which is hereby incorporated by reference. The test strip was modified from that described in U.S. Pat. No. 5,997,817, however, by the use of a different reagent. The nitrosoaniline reagent used had the composition described in Tables III and IV.

TABLE III Reagent Mass Composition - Prior to Dispense and Drying Mass for Component % w/w 1 kg Solid Polyethylene oxide (300 kDa) 0.8054% 8.0539 g Solid Natrosol 250M 0.0470% 0.4698 g Solid Avicel RC-591F 0.5410% 5.4104 g Solid Monobasic potassium phosphate 1.1437% 11.4371 g (annhydrous) Solid Dibasic potassium phosphate 1.5437% 15.4367 g (annhydrous) Solid Disodium Succinate hexahydrate 0.5876% 5.8761 g Solid Potassium Hydroxide 0.3358% 3.3579 g Solid Quinoprotein glucose 0.1646% 1.6464 g dehydrogenase (EnzC#: 1.1.99.17) Solid PQQ 0.0042% 0.0423 g Solid Trehalose 1.8875% 18.8746 g Solid Mediator 31.1144 0.6636% 6.6363 g Solid Triton X-100 0.0327% 0.3274 g solvent Water 92.2389% 922.3888 g % Solids 0.1352687 Target pH 6.8 Specific Enzyme Activity Used (U/mg) 689 DCIP Dispense Volume per Sensor 4.6 mg

TABLE IV Reagent Layer Composition - After Drying Mass per Component % w/w Sensor Solid Polyethylene oxide (300 kDa) 10.3829% 37.0480 ug Solid Natrosol 250M 0.6057% 2.1611 ug Solid Avicel RC-591F 6.9749% 24.8877 ug Solid Monobasic potassium phosphate 14.7445% 52.6107 ug (annhydrous) Solid Dibasic potassium phosphate 19.9006% 71.0087 ug (annhydrous) Solid Disodium Succinate hexahydrate 7.5753% 27.0299 ug Solid Potassium Hydroxide 4.3289% 15.4462 ug Solid Quinoprotein glucose dehydrogenase 2.1225% 7.5734 ug (EnzC#: 1.1.99.17) Solid PQQ 0.0546% 0.1947 ug Solid Trehalose 24.3328% 86.8243 ug Solid Mediator BM 31.1144 8.5553% 30.5268 ug Solid Triton X-100 0.4220% 1.5059 ug

The method for the manufacture of the glucose biosensor for this Example 4 is the same in all respects as disclosed in U.S. Pat. No. 5,997,817 except for the manufacture of the reagent. A protocol for the preparation of the preferred embodiment nitrosoaniline reagent is as follows:

-   Step 1: Prepare a buffer solution by adding 1.54 g of dibasic     potassium phosphate (anhydrous) to 43.5 g of deionized water. Mix     until the potassium phosphate is dissolved. -   Step 2: To the solution from step 1, add 1.14 g of monobasic     potassium phosphate and mix until dissolved. -   Step 3: To the solution from step 2, add 0.59 g of disodium     succinate (hexahydrate) and mix until dissolved. -   Step 4: Verify that the pH of the solution from step 3 is 6.7+/−0.1.     Adjustment should not be necessary. -   Step 5: Prepare a 5 g aliquot of the solution from step 4, and to     this add 113 kilounits (by DCIP assay) of the apoenzyme of     quinoprotein glucose dehydrogenase (EC#: 1.1.99.17). This is     approximately 0.1646 g. Mix, slowly, until the protein is dissolved. -   Step 6: To the solution from step 5, add 4.2 milligrams of PQQ and     mix for no less than 2 hours to allow the PQQ and the apoenzyme to     reassociate in order to provide functional enzyme. -   Step 7: To the solution from step 4, add 0.66 g of the mediator     precursor, N,N-bis(hydroxyethyl)-3-methoxy-4-nitrosoaniline     (hydrochloride) (BM 31.1144). Mix until dissolved (this solution     will have a greenish black coloration). -   Step 8: Measure the pH of the solution from step 7 and adjust the pH     to a target of 7.0+/−0.1. Normally this is accomplished with 1.197 g     of 5N potassium hydroxide. Because the specific amount of potassium     hydroxide may vary as needed to reach the desired pH, generally     deviations in mass from the 1.197 g are made up from an aliquot of     3.309 g deionized water which is also added at this step. -   Step 9: Prepare a solution of Natrosol 250M (available from     Aqualon), by slowly sprinkling 0.047 g over 44.57 g of deionized     water which is mixed (using a rotary mixer and blade impeller) at a     rate of approximately 600 rpm in a vessel of sufficient depth such     that the rotor blades are not exposed nor the solution running over.     Mix until the Natrosol is completely dissolved. -   Step 10: Prepare a suspension of Avicel RC-591F (available from     FMS), by slowly sprinkling 0.54 g onto the surface of the solution     from step 9, mixing at a rate of approximately 600 rpm for not less     than 60 minutes before proceeding. -   Step 11: To the suspension from step 10, gradually add 0.81 g of     Polyethylene oxide of 300 kDa mean molecular weight while mixing and     continue to mix for not less than 60 minutes before proceeding. -   Step 12: Gradually add the solution from step 8 to the suspension     from step 11 while mixing. Reduce the mixing rate to 400 rpm. -   Step 13: To the reagent from step 12, add 1.89 g of Trehalose and     continue mixing for not less than 15 minutes. -   Step 14: To the reagent from step 13, add 32.7 mg of Triton X-100     (available from Roche Diagnostics) and continue mixing. -   Step 15: To the reagent from step 14, add the enzyme solution from     step 6. Mix for no less than 30 minutes. At this point the reagent     is complete. At room temperature the wet reagent mass is considered     acceptable for use for 24 hours.

Spiked venous blood samples were used. Five levels of glucose, four temperatures (19, 23, 32 and 38° C.) and five levels of hematocrit (20, 30, 45, 60 and 70%) were independently varied, producing a covariance study with 100 samples. 16 test strips 300 were tested for each unique combination of glucose, temperature and hematocrit. The blood samples were applied to test strip 300 and the excitation potentials illustrated in FIG. 13 were applied to the electrodes. The excitation comprised a 3.2 kHz AC signal for approximately 4.0 seconds, a 2.13 kHz AC signal for approximately 0.1 seconds, a 1.07 kHz AC signal for approximately 0.1 seconds, a 200 Hz AC signal for approximately 0.1 seconds, a 25 Hz AC signal for approximately 0.1 seconds, followed by a DC signal of 550 mV for approximately 1.0 second. All four AC signals had an amplitude of 56.56 mV peak. The Total Test Time was 5.5 seconds from sample application time.

In this Example 4, the AC response of the sample was derived as admittance (the inverse of impedance). The admittance response is proportionate to the hematocrit level of the sample in a temperature dependent manner. The relationship between admittance, hematocrit and testing temperature is illustrated in FIG. 14. As compared to the test strip architecture of Example 2, the orthogonality of the temperature and hematocrit influence on glucose was not as strong in this Example 4; therefore a cross product term (T×HCT) was added to the admittance regression formula used in FIG. 14. The data used for the admittance charted in FIG. 14 is the last admittance measurement made for each sample during the 3.2 kHz AC portion of the excitation illustrated in FIG. 13.

Regression analysis of this data allows admittance, hematocrit and temperature to be related according to the following formula: H _(est)=(Y _(3.2kHz) +c ₀ +c ₁ dT)/(c ₂ dT+c ₃)  (Equation 7) It was determined that the admittance measurement made at 3.2 kHz was best correlated with hematocrit for this test system. Using this relationship to predict the blood hematocrit is accomplished using test temperature data reported by the temperature sensor in the meter and the measured admittance. In Equation 7, c₀, c₁, c₂ and c₃ are constants, dT is the deviation in temperature from a center defined as “nominal” (24° C. for example), and H_(est) is the estimated deviation in hematocrit from a similar “nominal” value. For the present purposes, the actual hematocrit value is not necessary, and it is generally preferred to produce a response which is proportionate but centers around a nominal hematocrit. Thus, for a 70% hematocrit, the deviation from a nominal value of 42% would be 28%, while conversely for a 20% hematocrit the deviation from the same nominal value would be −22%.

By using the AC admittance measurement to estimate the hematocrit level using Equation 7, the accuracy of the DC glucose response can be greatly improved by combining the estimated hematocrit, temperature and DC response to correct for the hematocrit interference in the DC response as follows (same as Equation 2 above): PRED=(a ₀ +hct ₁ H _(est) +hct ₂ H _(est) ²+tau₁ dT+tau₂ dT ²)+(a ₁ DC)(1+hct ₃ H _(est) +hct ₄ H _(est) ²)(1+tau₃ dT+tau₄ dT ²)  (Equation 8) The constants in Equation 8 can be determined using regression analysis, as is known in the art.

FIG. 15 illustrates the uncompensated 5.5 second DC glucose response of all of the blood samples as hematocrit and temperature vary (ignoring the AC measurement data). As will be appreciated, there is a wide variation in the DC current response as temperature and hematocrit vary. FIG. 16 illustrates the correlation between the actual blood glucose level of the sample versus the predicted response using Equation 8. As can be seen, when the DC response is compensated for hematocrit levels using the AC response data, an overall r² value of 0.9818 is achieved with a Total Test Time of 5.5 seconds. This demonstrates the applicability of the present method in achieving high accuracy and fast test times with a different reagent class than was used in Examples 1-3.

EXAMPLE 5 Combined AC and DC Measurement Using a 0.397 μl Sample

The measurement methods described herein have been found to be useful with other test strip designs as well. Example 5 was conducted using the test strip design illustrated in FIGS. 17A-B, and indicated generally at 1700. Referring to FIG. 17A, the test strip 1700 comprises a bottom foil layer 1702 formed from an opaque piece of 350 μm thick polyester (in the preferred embodiment this is Melinex 329 available from DuPont) coated with a 50 nm conductive (gold) layer (by sputtering or vapor deposition, for example). Electrodes and connecting traces are then patterned in the conductive layer by a laser ablation process to form working, counter, and dose sufficiency electrodes (described in greater detail hereinbelow) as shown. The laser ablation process is performed by means of an excimer laser which passes through a chrome-on-quartz mask. The mask pattern causes parts of the laser field to be reflected while allowing other parts of the field to pass through, creating a pattern on the gold which is ejected from the surface where contacted by the laser light.

Examples of the use of laser ablation techniques in preparing electrodes for biosensors are described in U.S. patent application Ser. No. 09/866,030, “Biosensors with Laser Ablation Electrodes with a Continuous Coverlay Channel” filed May 25, 2001, and in U.S. patent application Ser. No. 09/411,940, entitled “Laser Defined Features for Patterned Laminates and Electrode,” filed Oct. 4, 1999, both disclosures incorporated herein by reference.

The bottom foil layer 1702 is then coated in the area extending over the electrodes with a reagent layer 1704 in the form of an extremely thin reagent film. This procedure places a stripe of approximately 7.2 millimeters width across the bottom foil 1702 in the region labelled “Reagent Layer” on FIG. 17. In the present Example, this region is coated at a wet-coat weight of 50 grams per square meter of coated surface area leaving a dried reagent less than 20 μm thick. The reagent stripe is dried conventionally with an in-line drying system where the nominal air temperature is at 110° C. The rate of processing is nominally 30-38 meters per minute and depends upon the rheology of the reagent.

The materials are processed in continuous reels such that the electrode pattern is orthogonal to the length of the reel, in the case of the bottom foil 1702. Once the bottom foil 1702 has been coated with reagent, the spacer is slit and placed in a reel-to-reel process onto the bottom foil 1702. Two spacers 1706 formed from 100 μm polyester (in the preferred embodiment this is Melinex 329 available from DuPont) coated with 25 μm PSA (hydrophobic adhesive) on both the dorsal and ventral surfaces are applied to the bottom foil layer 1702, such that the spacers 1706 are separated by 1.5 mm and the working, counter and dose sufficiency electrodes are centered in this gap. A top foil layer 1708 formed from 100 μm polyester coated with a hydrophilic film on its ventral surface (using the process described in U.S. Pat. No. 5,997,817) is placed over the spacers 1706. In the preferred embodiment, the hydrophilic film is coated with a mixture of Vitel and Rhodapex surfactant at a nominal thickness of 10 microns. The top foil layer 1708 is laminated using a reel-to-reel process. The sensors can then be produced from the resulting reels of material by means of slitting and cutting.

The 1.5 mm gap in the spacers 1706 therefore forms a capillary fill space between the bottom foil layer 1702 and the top foil layer 1708. The hydrophobic adhesive on the spacers 1706 prevents the test sample from flowing into the reagent under the spacers 1706, thereby defining the test chamber volume. Because the test strip 1700 is 5 mm wide and the combined height of the spacer 1706 and conductive layer is 0.15 mm, the sample receiving chamber volume is 5 mm×1.5 mm×0.15 mm=1.125 μl  (Equation 9)

As shown in FIG. 17B, the distance from the sample application port 1710 and the dose sufficiency electrodes is 1.765 mm. The volume of sample needed to sufficiently cover the working, counter and dose sufficiency electrodes (i.e. the minimum sample volume necessary for a measurement) is 1.5 mm×1.765 mm×0.15 mm=0.397 μl  (Equation 10)

The reagent composition for the test strip 1700 is given in Tables V and VI.

TABLE V Reagent Mass Composition - Prior to Dispense and Drying Mass for Component % w/w 1 kg Solid Polyethylene oxide (300 kDa) 1.0086% 10.0855 g Solid Natrosol 250M 0.3495% 3.4954 g Solid Carboxymethylcellulose 7HF 0.3495% 3.4954 g Solid Monobasic potassium phosphate 0.9410% 9.4103 g (annhydrous) Solid Dibasic potassium phosphate 1.6539% 16.5394 g (trihydrous) Solid Disodium Succinate hexahydrate 0.2852% 2.8516 g Solid Potassium Hydroxide 0.2335% 2.3351 g Solid Quinoprotein glucose 0.3321% 3.3211 g dehydrogenase (EnzC#: 1.1.99.17) Solid PQQ 0.0093% 0.0925 g Solid Trehalose 0.7721% 7.7210 g Solid Mediator 31.1144 0.6896% 6.8956 g Solid Triton X-100 0.0342% 0.3419 g solvent Water 93.7329% 937.3293 g % Solids 6.6585% Target pH 7 Specific Enzyme Activity Used (U/mg) 689 DCIP Wet Reagent Coat Weight per Sensor (ug/mm²) 50

TABLE VI Reagent Layer Composition - After Drying Mass per Component % w/w Sensor* Solid Polyethylene oxide (300 kDa) 15.1469% 3.7821 ug Solid Natrosol 250M 5.2495% 1.3108 ug Solid Carboxymethylcellulose 7HF 5.2495% 1.3108 ug Solid Monobasic potassium phosphate 14.1328% 3.5289 ug (annhydrous) Solid Dibasic potassium phosphate 24.8395% 6.2023 ug (trihydrous) Solid Disodium Succinate hexahydrate 4.2827% 1.0694 ug Solid Potassium Hydroxide 3.5069% 0.8757 ug Solid Quinoprotein glucose dehydrogenase 4.9878% 1.2454 ug (EnzC#: 1.1.99.17) Solid PQQ 0.1390% 0.0347 ug Solid Trehalose 11.5958% 2.8954 ug Solid Mediator BM31.1144 10.3562% 2.5859 ug Solid Triton X-100 0.5135% 0.1282 ug *“Mass per Sensor” is the amount of the component within the capillary; this does not reflect the reagent that is outside of the capillary.

A protocol for the preparation of the preferred embodiment nitrosoaniline reagent is as follows:

-   Step 1: Prepare a buffer solution by adding 1.654 g of dibasic     potassium phosphate (trihydrous) to 31.394 g of deionized water. Mix     until the potassium phosphate is dissolved. -   Step 2: To the solution from step 1, add 0.941 g of monobasic     potassium phosphate and mix until dissolved. -   Step 3: To the solution from step 2, add 0.285 g of disodium     succinate (hexahydrate) and mix until dissolved. -   Step 4: Verify that the pH of the solution from step 3 is 6.8+/−0.1.     Adjustment should not be necessary. -   Step 5: Prepare a 4.68 g aliquot of the solution from step 4, and to     this add 229 kilounits (by DCIP assay) of the apoenzyme of     quinoprotein glucose dehydrogenase (EC#: 1.1.99.17). This is     approximately 0.3321 g. Mix, slowly, until the protein is dissolved. -   Step 6: To the solution from step 5, add 9.3 milligrams of PQQ and     mix for no less than 2 hours to allow the PQQ and the apoenzyme to     reassociate in order to provide functional enzyme. -   Step 7: Prepare a solution by dissolving 0.772 g of Trehalose into     1.218 g of deionized water. -   Step 8: After enzyme reassociation, add the solution from step 7 to     the solution from step 6 and continue mixing for not less than 30     minutes. -   Step 9: To the solution from step 4, add 0.690 g of the mediator     precursor BM 31.1144. Mix until dissolved (this solution will have a     greenish black coloration). -   Step 10: Measure the pH of the solution from step 9 and adjust the     pH to a target of 7.0+/−0.1. Normally this is accomplished with     1.006 g of 5N potassium hydroxide. Because the specific amount of     potassium hydroxide may vary as needed to reach the desired pH,     generally deviations in mass from the 1.006 g are made up from an     aliquot of 3.767 g deionized water which is also added at this step.     Step 11: Prepare a solution of Natrosol 250M (available from     Aqualon), by slowly sprinkling 0.350 g over 56.191 g of deionized     water which is mixed (using a rotary mixer and blade impeller) at an     initial rate of approximately 600 rpm in a vessel of sufficient     depth such that the rotor blades are not exposed nor the solution     running over. As the Natrosol dissolves, the mixing rate needs to be     increased to a speed of 1.2-1.4 krpm. Mix until the Natrosol is     completely dissolved. Note that the resulting matrix will be     extremely viscous—this is expected. -   Step 12: To the solution from step 11, gradually add 0.350 g of     Sodium-Carboxymethylcellulose 7HF (available from Aqualon). Mix     until the polymer is dissolved. -   Step 13: To the suspension from step 13, gradually add 1.01 g of     Polyethylene oxide of 300 kDa mean molecular weight while mixing and     continue to mix for not less than 60 minutes before proceeding. -   Step 14: Gradually add the solution from step 10 to the suspension     from step 13 while mixing. -   Step 15: To the reagent from step 14, add 34.2 mg of Triton X-100     (available from Roche Diagnostics) and continue mixing. -   Step 16: To the reagent from step 15, add the enzyme solution from     step 8. Mix for no less than 30 minutes. At this point the reagent     is complete. At room teperature the wet reagent mass is considered     acceptable for use for 24 hours.

The measurement results illustrated in FIG. 18 show the correlation coefficient r² between the DC current response and the glucose level as the Read Time varies for three combinations of temperature and hematocrit. These results demonstrate that a robust DC response should be anticipated for tests as fast as 1 second. However, those skilled in the art will recognise that there are undesirable variations in the sensor accuracy (correlation) due to the interfering effects of temperature and hematocrit levels, suggesting that the combined AC and DC measurement method of the present method should produce more closely correlated results.

Based upon the encouraging results obtained in FIG. 18, a further test was designed using the excitation signal of FIG. 19 applied to the test strip 1700. The excitation comprised a 10 kHz AC signal applied for approximately 1.8 seconds, a 20 kHz AC signal applied for approximately 0.2 seconds, a 2 Hz AC signal applied for approximately 0.2 seconds, a 1 Hz AC signal applied for approximately 0.2 seconds, and a DC signal applied for approximately 0.5 seconds. The AC signals had an amplitude of 12.7 mV peak, while the DC signal had an amplitude of 550 mV. The Total Test Time was 3.0 seconds.

A covariance study using spiked venous blood samples representing five glucose levels (40, 120, 200, 400 and 600), five hematocrit levels (20, 30, 45, 60 and 70%) and five temperatures (12, 18, 24, 32 and 44° C.) was designed, resulting in 125 separate combinations. As in the previous examples, the relationship between admittance, temperature and hematocrit was examined and plotted (FIG. 20 shows the admittance at 20 kHz versus hematocrit as temperature varies) and it was confirmed that the admittance was linearly related to hematocrit in a temperature dependent manner. An additional discovery, however, was that the phase angle of the AC response was correlated with hematocrit in a temperature independent manner. The phase angle of the 20 kHz AC response is plotted versus hematocrit in FIG. 21. The results for phase angle measured at 10 kHz are similar. The hematocrit of the blood sample may therefore be reliably estimated using only the phase angle information as follows: H _(est) =c ₀ +c ₁(Φ_(10kHz)−Φ_(20kHz))+c ₂(Φ_(2kHz)Φ_(1kHz))  (Equation 11)

For the test strip used in this Example 5, the correlation between phase angle and hematocrit was better at higher frequencies. Because of this, the c₂ constant approaches zero and H_(est) can reliably be estimated using only the 10 kHz and 20 kHz data. Use of lower frequencies, however, allows for slight improvements in the strip-to-strip variability of the H_(est) function. The present method therefore may be used to estimate hematocrit using only AC phase angle measurements preferably made at least one AC frequency, more preferably made at least two AC frequencies, and most preferably made at least four AC frequencies.

Because the hematocrit can be determined using only the AC response data, and we know from FIG. 20 that admittance is linearly related to hematocrit and temperature, we can now determine the temperature of the sample under analysis using only the AC response as follows: T _(est) =b ₀ +b ₁(Y _(10kHz) −Y _(20kHz))+b ₂(Y _(2kHz) −Y _(1kHz))+b ₃ H _(est)  (Equation 12) where b₀, b₁, b₂ and b₃ are constants. It will be appreciated that the estimation of hematocrit and temperature from the AC response data may be made with more or fewer frequency measurements, and at different frequencies than those chosen for this example. The particular frequencies that produce the most robust results will be determined by test strip geometries and dimensions. The devices and methods described herein therefore may be used to estimate test sample temperature using only AC response measurements preferably made at least one AC frequency, more preferably made at least two AC frequencies, and most preferably made at least four AC frequencies.

Those skilled in the art will recognise that the direct measurement of the temperature of the sample under test (by means of the AC response) is a great improvement over prior art methods for estimating the temperature of the sample. Typically, a thermistor is placed in the test meter near where the test strip is inserted into the meter. Because the thermistor is measuring a temperature remote from the actual sample, it is at best only a rough approximation of the true sample temperature. Furthermore, if the sample temperature is changing (for example due to evaporation), then the thermal inertia of the test meter and even the thermistor itself will prevent the meter-mounted thermistor from accurately reflecting the true temperature of the sample under test. By contrast, the temperature estimation of the present method is derived from measurements made within the sample under test (i.e. within the reaction zone in which the sample under test reacts with the reagent), thereby eliminating any error introduced by the sample being remote from the measuring location. Additionally, the temperature estimation of the present method is made using data that was collected very close in time to the glucose measurement data that will be corrected using the temperature estimation, thereby further improving accuracy. This represents a significant improvement over the prior art methods.

As a demonstration of the effectiveness of the method of this Example 5 for correcting for the effects of interferants on the blood glucose measurement, the uncompensated DC current response versus known glucose concentration is plotted in FIG. 22 for all 125 combinations of glucose, temperature and hematocrit (the AC measurements were ignored when plotting this data). As will be appreciated by those skilled in the art, the data exhibits huge variation with respect to hematocrit and temperature.

As previously discussed, the accuracy of the DC glucose response can be greatly improved by combining the estimated hematocrit, temperature and DC response to correct for the hematocrit and temperature interference in the DC response as follows: PRED=(a ₀ +hct ₁ H _(est) +hct ₂ H _(est)+tau₁ T _(est)+tau₂ T _(est))+(a ₁ DC)(1+hct ₃ H _(est) +hct ₄ H _(est) ²)(1+tau₃ T _(est)+tau₄ T _(est))  (Equation 13) The constants in Equation 13 can be determined using regression analysis, as is known in the art. The present method therefore allows one to estimate hematocrit by using the AC phase angle response (Equation 11). The estimated hematocrit and the measured AC admittance can be used to determine the estimated temperature (Equation 12). Finally, the estimated hematocrit and estimated temperature can be used with the measured DC response to obtain the predicted glucose concentration (Equation 13).

Applying the above methodology to the test data plotted in FIG. 22, we obtain the predicted glucose versus DC current response illustrated in FIG. 23. This data represents 125 covariant samples having hematocrit levels ranging from 20%-70% and temperatures ranging from 12° C.-44° C. Even with these wide variations in interferant levels, the measurement method described produced an overall r² correlation of 0.9874 using a 3.0 second Total Test Time.

EXAMPLE 6 Simultaneous AC and DC Measurement Using a 0.397 μl Sample

Using the same test strip 1700 and reagent described above for Example 5, the excitation profile illustrated in FIG. 24 was utilized in order to decrease the Total Test Time. As described above with respect to Example 5, it was determined that the phase angle at 20 kHz and at 10 kHz were most closely correlated with the hematocrit estimation. It was therefore decided to limit the AC portion of the excitation to these two frequencies in Example 6 in order to decrease the Total Test Time. In order to make further reductions in Total Test Time, the 10 kHz AC excitation was applied simultaneously with the DC signal (i.e. an AC signal with a DC offset), the theory being that this combined mode would allow for the collection of simultaneous results for DC current, AC phase and AC admittance, providing the fastest possible results. Therefore, the 20 kHz signal was applied for 0.9 seconds. Thereafter, the 10 kHz and DC signals were applied simultaneously for 1.0 second after a 0.1 second interval.

For this Example 6, 49 spiked venous blood samples representing seven glucose levels and seven hematocrit levels were tested. The correlation coefficient r² between the DC current and the blood hematocrit was then examined at three DC measurement times: 1.1 seconds, 1.5 seconds and 1.9 seconds after sample application. These correlations are plotted versus hematocrit level in FIG. 25. All of these results are comparable, although the correlation is generally poorest at 1.1 seconds and generally best at 1.5 seconds. The minimum correlation coefficient, however, exceeds 0.99.

FIG. 26 illustrates the phase angle at 20 kHz plotted against hematocrit levels. The correlation between these two sets of data is very good, therefore it was decided that the 10 kHz data was unnecessary for estimating hematocrit. The hematocrit can therefore be estimated solely from the 20 kHz phase angle data as follows: H _(est) =c ₀ +c ₁Φ_(20kHz)  (Equation 14)

FIG. 27 illustrates the DC current response versus glucose level for all measured hematocrit levels as the read time is varied between 1.1 seconds, 1.5 seconds and 1.9 seconds. Not surprisingly, the DC current at 1.1 seconds is greater than the DC current at 1.5 seconds, which is greater than the DC current at 1.9 seconds. Those skilled in the art will recognise that the hematocrit level has a large effect on the DC current, particularly at high glucose concentrations.

As discussed hereinabove, the accuracy of the DC glucose response can be greatly improved by compensating for the interference caused by hematocrit as follows: PRED=(a ₀ +hct ₁ H _(est) +hct ₂ H _(est) ²)+(a ₁ DC)(1+hct ₃ H _(est) +hct ₄ H _(est) ²)  (Equation 15) Note that Equation 15 does not include temperature compensation terms since temperature variation was not included in the experiment of this Example 6, it can be reasonably inferred from previous examples that a Test term could be included using the 10 kHz and 20 kHz admittance values in combination with the H_(est) term. Because the hematocrit can be reliably estimated using only the 20 kHz phase angle measurement data, the hematocrit compensated predicted glucose response can be determined using only this phase angle information and the measured DC response. The compensated DC response versus glucose level for only the DC read at 1.1 seconds (representing a 1.1 second Total Test Time) is illustrated in FIG. 28. The data shows an overall r² correlation of 0.9947 with a 1.1 second Total Test Time.

The same data for the 1.5 second DC read is illustrated in FIG. 29, showing an overall r² correlation of 0.9932 for a 1.5 second Total Test Time. The same data for the 1.9 second DC read is illustrated in FIG. 30, showing an overall r² correlation of 0.9922 for a 1.9 second Total Test Time. Surprisingly, the r² correlation actually decreased slightly with the longer test times. Notwithstanding this, the correlation coefficients for all three compensated data sets—where all 7 hematocrits ranging from 20% through 60% are combined—were in excess of 0.99, demonstrating the applicability of the present method to yield a blood glucose test as fast as 1.1 seconds, combined with improved accuracy, where the sensor requires less than 0.4 microliters of blood in order to perform the glucose measurement test.

EXAMPLE 7 Use of AC Phase Angle to Detect an Abused Sensor

In order to provide an extra measure of quality control to the analyte measurement process, particularly when the test system is to be used by a non-professional end user, it is desirable to detect sensors (test strips) that have been mis-dosed (double dosed, etc.), that have been previously used, or that have degraded enzymes (from being stored in too humid an environment, being too old, etc.). These conditions are collectively referred to as “abused sensors.” It is desired to devise a test that will abort the analyte measurement process (or at least warn the user that the test results may not be accurate) if an abused sensor is inserted into the test meter.

When performing a blood glucose analysis, the test meter will typically make several successive current measurements as the blood sample continues to react with the reagent chemistry. As is well known in the art, this response current is known as the Cottrell current and it follows a pattern of decay as the reaction progresses. We may define a Cottrell Failsafe Ratio (CFR) as follows:

The Cottrell response of the biosensor in the Confidence system can be given by:

$\begin{matrix} {I_{\;{cottrell}} = {\frac{{nFA}\sqrt{D}}{\sqrt{\Pi}}{Ct}^{\alpha}}} & \left( {{Equation}\mspace{14mu} 16} \right) \end{matrix}$

-   -   where: n=electrons freed per glucose molecule         -   F=Faraday's Constant         -   A=Working electrode surface area         -   t=elapsed time since application of excitation         -   D=diffusion coefficient         -   C=glucose concentration         -   α=a cofactor-dependent constant.             All of the parameters of this equation will normally be             constant for the sensor except the glucose concentration and             time. We can therefore define a normalized Cottrell failsafe             ratio (NCFR) as:

$\begin{matrix} {{N\; C\; F\; R} = {\frac{\sum\limits_{k = 1}^{m}I_{k}}{{mI}_{m}} = {\frac{\sum\limits_{k = 1}^{m}{\frac{{nFA}\sqrt{D}}{\sqrt{\Pi}}{Ct}_{k}^{\alpha}}}{m\frac{{nFA}\sqrt{D}}{\sqrt{\Pi}}{Ct}_{m}^{\alpha}} = {\frac{\sum\limits_{k = 1}^{m}t_{k}^{\alpha}}{{mt}_{m}^{\alpha}} = {Constant}}}}} & \left( {{Equation}\mspace{14mu} 17} \right) \end{matrix}$

As the time terms in this equation are known and constant for a sensor measurement, the ratio always yields a constant for Cottrell curves with identical sample times and intervals. Therefore, the sum of sensor currents divided by the last sensor current should yield a constant independent of glucose concentration. This relationship is used in the preferred embodiment to detect potentially faulty biosensor responses.

A Current Sum Failsafe can be devised that places a check on the Cottrell response of the sensor by summing all of the acquired currents during sensor measurement. When the final current is acquired, it is multiplied by two constants (which may be loaded into the meter at the time of manufacture or, more preferably, supplied to the meter with each lot of sensors, such as by a separate code key or by information coded onto the sensor itself). These constants represent the upper and lower threshold for allowable NCFR values.

The two products of the constants multiplied by the final current are compared to the sum of the biosensor currents. The sum of the currents should fall between the two products, thereby indicating that the ratio above was fulfilled, plus or minus a tolerance.

Therefore, the preferred embodiment performs the following check when there is a single DC block:

$\begin{matrix} {{\left( I_{m} \right)\left( C_{1} \right)} \leq {\sum\limits_{k = 1}^{m}I_{k}} \leq {\left( I_{m} \right)\left( C_{u} \right)}} & \left( {{Equation}\mspace{14mu} 18} \right) \end{matrix}$

-   -   where C_(u)=upper constant from the Code Key         -   C_(l)=lower constant from the Code Key         -   I_(m)=final biosensor current

Because some embodiments may contain two DC blocks in the measurement sequence, a Modified Cottrell Failsafe Ratio (MCFR) can be formulated as:

$\begin{matrix} {{M\; C\; F\; R} = \frac{{w_{1}N\; C\; F\; R_{1}} + {w_{2}N\; C\; F\; R_{2}}}{w_{1} + w_{2}}} & \left( {{Equation}\mspace{20mu} 19} \right) \end{matrix}$

where w₁, w₂=weighting constants (e.g. from the Code Key)

-   -   NCFR₁, NCFR₂=the Normalized Cottrell Failsafe Ratios for DC         blocks 1 and 2 respectively.         Therefore, the preferred embodiment performs the following check         when there are two DC blocks:

$\begin{matrix} {{\left( {w_{1} + w_{2}} \right)I_{m_{1}}I_{m_{2}}C_{L}} \leq \left( {{w_{1}I_{m_{2}}{\sum\limits_{k = 1}^{m_{1}}I_{k}}} + {w_{2}I_{m_{1}}{\sum\limits_{k = 1}^{m_{2}}I_{k}}}} \right) \leq {\left( {w_{1} + w_{2}} \right)I_{m_{1}}I_{m_{2}}C_{u}}} & \left( {{Equation}\mspace{14mu} 20} \right) \end{matrix}$

-   -   where C_(u)=upper constant from the Code Key         -   C_(L)=lower constant from the Code Key         -   I_(m1), I_(m2)=final biosensor current in DC blocks 1 and 2

The NCFR (and MCFR) is correlated with hematocrit. As demonstrated hereinabove in Example 3, the AC phase angle is also correlated with hematocrit. It follows then, that the AC phase angle and the NCFR are correlated with one another. This relationship holds only if the sensor is unabused. The correlation degrades for an abused sensor.

It is therefore possible to design an equation to analyze the measured phase angle data to produce a failsafe calculation that will indicate if an abused sensor is being used. In the preferred embodiment, it was chosen to use the difference between the phase angles measured at two separate frequencies in order to make the test more robust to errors caused by parasitic resistance, etc. Applying the arctangent function to drive the two populations to different asymptotes yields the following failsafe equation: FAILSAFE=1000×arctan[NCFR/(fs ₀ +fs ₁(Φ_(10kHz)−Φ_(20kHz)))]  (Equation 21) where 1000=scaling factor

NCFR=Cottrell Failsafe Ratio

fs₀=linear regression intercept

fs₁=linear regression slope

Φ_(10kHz)=phase angle at 10 kHz

Φ_(20kHz)=phase angle at 20 kHz

Using Equation 21, the intercept term fs₀ can be chosen such that a FAILSAFE value below zero indicates an abused sensor, while a FAILSAFE value above zero indicates a non-abused sensor. Those skilled in the art will recognise that the opposite result could be obtained by choosing a different intercept.

Use of Dose Sufficiency Electrodes

As described hereinabove, it has been recognised that accurate sample measurement requires adequate coverage of the measurement electrodes by the sample. Various methods have been used to detect the insufficiency of the sample volume in the prior art. For example, the Accu-Chek® Advantage® glucose test meter sold by Roche Diagnostics Corporation of Indianapolis, Ind. warned the user of the possible inadequacy of the sample volume if non-Cotrellian current decay was detected by the single pair of measurement electrodes. Users were prompted to re-dose the test strip within a specified time allotment.

The possibility of insufficient sample size has been heightened in recent years due to the use of capillary fill devices used in conjunction with blood lancing devices designed to minimize pain through the requirement of only extremely small sample volumes. If an inadequate amount of sample is drawn into the capillary fill space, then there is a possibility that the measurement electrodes will not be adequately covered and the measurement accuracy will be compromised. In order to overcome the problems associated with insufficient samples, various prior art solutions have been proposed, such as placing an additional electrode downstream from the measurement electrodes; or a single counter electrode having a sub-element downstream and major element upstream of a working electrode; or an indicator electrode arranged both upstream and downstream from a measurement electrode (allowing one to follow the flow progression of the sample across the working and counter electrodes or the arrival of the sample at a distance downstream). The problem associated with each of these solutions is that they each incorporate one or the other electrode of the measurement pair in communication with either the upstream or the downstream indicator electrodes to assess the presence of a sufficient volume of sample to avoid biased test results.

Despite these prior art design solutions, failure modes persist wherein the devices remain prone to misinterpretation of sample sufficiency. The present inventors have determined that such erroneous conclusions are related primarily to the distances between a downstream member of a measurement electrode pair (co-planar or opposing geometries) and the dose detection electrode, in combination with the diversity of non-uniform flow fronts. A sample traversing the capillary fill space having an aberrant (uneven) flow front can close the circuit between a measurement electrode and an indicator electrode and erroneously advise the system that sufficient sample is present to avoid a biased measurement result.

Many factors employed in the composition and/or fabrication of the test strip capillary fill spaces influence such irregular flow front behavior. These factors include:

-   -   disparities between surface energies of different walls forming         the capillary fill space.     -   contamination of materials or finished goods in the test strip         manufacturing facility.     -   unintentional introduction of a contaminant from a single         component making up the walls of the capillary fill space (an         example being a release agent (typically silicon) that is common         to manufacturing processes wherein release liners are used).     -   hydrophobic properties of adhesives (or contaminated adhesives)         used in the lamination processes.     -   disparate surface roughnesses on the walls of the capillary fill         space.     -   dimensional aspect ratios.     -   contaminated mesh materials within the capillary fill space.     -   non-homogeneous application of surfactants onto mesh materials         within the capillary fill space.

Another problem with prior art dose sufficiency methodologies determined by the present inventors relates to the use of one or the other of the available measurement electrodes in electrical communication with an upstream or downstream dose detection electrode. In such arrangements, the stoichiometry of the measurement zone (the area above or between the measurement electrodes) is perturbed during the dose detect/dose sufficiency test cycle prior to making a measurement of the analyte of interest residing in the measurement zone. As sample matrices vary radically in make-up, the fill properties of these samples also vary, resulting in timing differences between sample types. Such erratic timing routines act as an additional source of imprecision and expanded total system error metrics.

Trying to solve one or more of these obstacles typically can lead to 1) more complex manufacturing processes (additional process steps each bringing an additional propensity for contamination); 2) additional raw material quality control procedures; 3) more costly raw materials such as laminate composites having mixtures of hydrophobic and hydrophyllic resins and negatively impacting manufacturing costs; and 4) labor-intensive surfactant coatings of meshes and or capillary walls.

EXAMPLE 8 Determination of Fluid Flow Front Behavior in a Capillary Fill Space

In order to design an electrode system that will adequately indicate dose sufficiency in a test strip employing a capillary fill space, an experiment was performed to examine the flow front shape at the leading edge of the sample as it progresses through the capillary fill space. Test fixtures comprising two sheets of clear polycarbonate sheets joined together with double-sided adhesive tape were used, where the capillary fill space was formed by cutting a channel in the double-sided tape. Use of the polycarbonate upper and lower sheets allowed the flow fronts of the sample to be videotaped as it flowed through the capillary fill space.

Specifically, the test devices were laminated using laser cut 1 mm thick Lexan® polycarbonate sheets (obtained from Cadillac Plastics Ltd., Westlea, Swindon SN5 7EX, United Kingdom). The top and bottom polycarbonate sheets were coupled together using double-sided adhesive tapes (#200 MP High Performance acrylic adhesive obtained from 3M Corporation, St. Paul, Minn.). The capillary channels were defined by laser cutting the required width openings into the double-sided tape. Tape thicknesses of 0.05 μm, 0.125 μm, and 0.225 μm were used to give the required channel heights. The dimensions of the capillary spaces of the test devices are tabulated in FIG. 31.

The top and bottom polycarbonate parts were laminated together with the laser cut adhesive tapes using a custom-built jig to ensure reproducible fabrication. For each test device, a fluid receptor region defining the entrance to the capillary channel was formed by an opening pre-cut into the upper polycarbonate sheet and adhesive tape components. For each of the three channel heights, channel widths of 0.5 mm, 1.00 mm, 1.5 mm, 2.00 mm, 3.00 mm, and 4.00 mm were fabricated. The capillary channel length for all devices was 50 mm. Twenty-eight (28) of each of the eighteen (18) device types were constructed. The assembled devices were plasma treated by Weidman Plastics Technology of Dortmund, Germany. The following plasma treatment conditions were used:

-   Processor: Microwave plasma processor 400 -   Microwave Power: 600 W -   Gas: O₂ -   Pressure: 0.39 miilibar -   Gas Flow: 150 ml/min -   Time: 10 minutes -   Surface Energy Pre-Treatment: <38 mN/m -   Surface Energy Post-Treatment: 72 mN/m     The plasma-treated devices were stored at 2-8° C. when not in use.     The devices were allowed to equilibrate to room temperature for     one (1) hour minimum before use.

Each of the test devices was dosed with a fixed volume of venous blood having a hematocrit value of 45%. Flow and flow front behavior was captured on videotape for later analysis. It was determined that the relative dimensions of the capillary fill channel determined the flow front behavior. Devices to the left of the dashed line in FIG. 31 (devices A2, A4, B2, B4, B5, C2, C4, and C5) resulted in a convex flow front behavior, while devices to the right of the dashed line (devices A6, A8, A11, B6, B8, B11, C6, C8, and C11) displayed a concave flow front behavior. Both the convex and concave flow front behaviors are schematically illustrated in FIG. 31. This data shows that the aspect ratio between the height and the width of the capillary fill space is a determining factor in whether the sample flow front is convex or concave.

Use of Dose Sufficiency Electrodes Cont'd

The problems associated with a concave flow front in a capillary fill space are illustrated in FIGS. 32A-C. In each of the figures, the test strip includes a working electrode 3200, a reference electrode 3202, and a downstream dose sufficiency electrode 3204 that works in conjunction with one of the measurement electrodes 3200 or 3202. In addition to the measurement zone stoichiometry problems associated with the use of the dose sufficiency electrode 3204 in conjunction with one of the measurement electrodes discussed above, FIGS. 32A-C illustrate that a sample flow front exhibiting a concave shape can also cause biased measurement results. In each drawing, the direction of sample travel is shown by the arrow. In FIG. 32A, the portions of the sample adjacent to the capillary walls have reached the dose sufficiency electrode 3204, thereby electrically completing the DC circuit between this electrode and one of the measurement electrode pair that is being monitored by the test meter in order to make the dose sufficiency determination. Although the test meter will conclude that there is sufficient sample to make a measurement at this time, the sample clearly has barely reached the reference electrode 3202 and any measurement results obtained at this time will be highly biased.

Similarly, FIG. 32B illustrates the situation where the dose sufficiency electrode 3204 has been contacted (indicating that the measurement should be started), but the reference electrode 3202 is only partially covered by the sample. Although the sample has reached the reference electrode 3202 at this time, the reference electrode 3202 is not completely covered by sample, therefore any measurement results obtained at this time will be partially biased. Both of the situations illustrated in FIGS. 32A-B will therefore indicate a false positive for dose sufficiency, thereby biasing the measurement test results. Only in the situation illustrated in FIG. 32C, where the reference electrode 3202 is completely covered by the sample, will the measurement results be unbiased due to the extent of capillary fill in the measurement zone.

The embodiments described solve the stoichiometric problems associated with the prior art designs pairing the dose sufficiency electrode with one of the measurement electrodes when making the dose sufficiency determination. As shown in FIG. 33, the embodiment described comprehends a test strip having an independent pair of dose sufficiency electrodes positioned downstream from the measurement electrodes. The test strip is indicated generally as 3300, and includes a measurement electrode pair consisting of a counter electrode 3302 and a working electrode 3304. The electrodes may be formed upon any suitable substrate in a multilayer test strip configuration as is known in the art and described hereinabove. The multilayer configuration of the test strip provides for the formation of a capillary fill space 3306, also as known in the art. Within the capillary fill space 3306, and downstream (relative to the direction of sample flow) from the measurement electrodes 3302 and 3304 are formed a dose sufficiency working electrode 3308 and a dose sufficiency counter electrode 3310, together forming a dose sufficiency electrode pair.

When the test strip 3300 is inserted into the test meter, the test meter will continuously check for a conduction path between the dose sufficiency electrodes 3308 and 3310 in order to determine when the sample has migrated to this region of the capillary fill space. Once the sample has reached this level, the test meter may be programmed to conclude that the measurement electrodes are covered with sample and the sample measurement sequence may be begun. It will be appreciated that, unlike as required with prior art designs, no voltage or current need be applied to either of the measurement electrodes 3302 and 3304 during the dose sufficiency test using the test strip design of FIG. 33. Thus the stoichiometry of the measurement zone is not perturbed during the dose sufficiency test cycle prior to making a measurement of the analyte of interest residing in the measurement zone. This represents a significant improvement over other dose sufficiency test methodologies.

The test strip 3300 is also desirable for judging dose sufficiency when the capillary fill space is designed to produce samples that exhibit a convex flow front while filling the capillary fill space 3306, as illustrated in FIG. 34A. As can be seen, the measurement zone above the measurement electrodes 3302 and 3304 is covered with sample when the convex flow front reaches the dose sufficiency electrode pair 3308,3310. The test strip design 3300 may not, however, produce ideal results if the capillary fill space 3306 allows the sample to exhibit a concave flow front while filling, as shown in FIG. 34B. As can be seen, the peripheral edges of the concave flow front reach the dose sufficiency electrodes 3308,3310 before the measurement zone has been completely covered with sample. With DC or low frequency excitation (discussed in greater detail hereinbelow), the dose sufficiency electrodes 3308,3310 will indicate sample sufficiency as soon as they are both touched by the edges of the flow front. Therefore, the dose sufficiency electrode design shown in the test strip of FIG. 33 works best when the sample filling the capillary space 3306 exhibits a convex flow front.

It will be appreciated that the dose sufficiency electrodes 3308,3310 have their longest axis within the capillary fill space 3306 oriented perpendicular to the longitudinal axis of the capillary fill space 3306. Such electrodes are referred to herein as “perpendicular dose sufficiency electrodes.” An alternative dose sufficiency electrode arrangement is illustrated in FIGS. 35A-B. As shown in FIG. 35A, the present method also comprehends a test strip having an independent pair of dose sufficiency electrodes positioned downstream from the measurement electrodes, where the dose sufficiency electrodes have their longest axis within the capillary fill space oriented parallel to the longitudinal axis of the capillary fill space. Such electrodes are referred to herein as “parallel dose sufficiency electrodes.” The test strip in FIG. 35 is indicated generally as 3500, and includes a measurement electrode pair consisting of a counter electrode 3502 and a working electrode 3504. The electrodes may be formed upon any suitable substrate in a multilayer test strip configuration as is known in the art and described hereinabove. The multilayer configuration of the test strip provides for the formation of a capillary fill space 3506, also as known in the art. Within the capillary fill space 3506, and downstream (relative to the direction of sample flow) from the measurement electrodes 3502 and 3504 are formed a dose sufficiency working electrode 3508 and a dose sufficiency counter electrode 3510, together forming a parallel dose sufficiency electrode pair.

When the test strip 3500 is inserted into the test meter, the test meter will continuously check for a conduction path between the dose sufficiency electrodes 3508 and 3510 in order to determine when the sample has migrated to this region of the capillary fill space. Once the sample has reached this level, the test meter may be programmed to conclude that the measurement electrodes are covered with sample and the sample measurement sequence may be begun. It will be appreciated that, as with the test strip 3300 (and unlike as required with prior art designs), no voltage or current need be applied to either of the measurement electrodes 3502 and 3504 during the dose sufficiency test using the test strip design of FIG. 35. Thus the stoichiometry of the measurement zone is not perturbed during the dose sufficiency test cycle prior to making a measurement of the analyte of interest residing in the measurement zone. This represents a significant improvement over other dose sufficiency test methodologies.

A further improved operation is realized with the parallel dose sufficiency electrodes of the test strip 3500 when the dose sufficiency electrodes are energized with a relatively high frequency AC excitation signal. When a relatively high frequency AC signal is used as the dose sufficiency excitation signal, the dose sufficiency electrodes 3508,3510 display significant edge effects, wherein the excitation signal traverses the gap between the electrodes only when the electrode edges along the gap are covered with the sample fluid. The test strip 3500 is illustrated in enlarged size in FIG. 36 (with only the electrode portions lying within the capillary fill space 3506 and the strip-to-meter electrode contact pads visible). When one of the pair of dose sufficiency electrodes 3508,3510 is excited with an AC signal, the majority of the signal travels from one electrode edge to the edge of the other electrode (when the edges are covered with sample), rather than from the upper flat surface of one electrode to the upper flat surface of the other electrode. These paths of edge-to-edge electrical communication are illustrated schematically as the electric field lines 3602 in FIG. 36.

Higher AC frequencies produce the best edge-only sensitivity from the dose sufficiency electrodes. In the preferred embodiment, a 9 mV_(rms) (+/−12.7 mV peak-to-peak) excitation signal of 10 kHz is used to excite one of the dose sufficiency electrodes. The gap width GW between the edges of the dose sufficiency electrodes 3508, 3510 is preferably 100-300 μm, more preferably 150-260 μm, and most preferably 255 μm. A smaller gap width GW increases the amount of signal transmitted between dose sufficiency electrodes whose edges are at least partially covered by sample; however, the capacitance of the signal transmission path increases with decreasing gap width GW.

An advantage of the parallel dose sufficiency electrode design of FIGS. 35 and 36, when used with AC excitation, is that there is substantially no electrical communication between the electrodes until the sample covers at least a portion of the edges along the electrode gap. Therefore, a sample exhibiting the concave flow front of FIG. 35A, where the illustrated sample is touching both of the dose sufficiency electrodes 3508,3510 but is not touching the electrode edges along the gap, will not produce any significant electrical communication between the dose sufficiency electrodes. The test meter will therefore not form a conclusion of dose sufficiency until the sample has actually bridged the dose sufficiency electrodes between the electrode edges along the gap. This will happen only after the rear-most portion of the concave flow front has reached the dose sufficiency electrodes 3508,3510, at which point the sample has completely covered the measurement zone over the measurement electrodes. As can be seen in FIG. 35B, convex sample flow fronts will activate the dose sufficiency electrodes 3508, 3510 as soon as the flow front reaches the dose sufficiency electrodes (at which point the sample has completely covered the measurement zone over the measurement electrodes).

Another advantage to the parallel dose sufficiency electrodes illustrated in FIGS. 35 and 36 is that the amount of signal transmitted between the electrodes is proportional to the amount of the gap edges that is covered by the sample. By employing an appropriate threshold value in the test meter, a conclusion of dose sufficiency can therefore be withheld until the sample has covered a predetermined portion of the dose sufficiency electrode gap edge. Furthermore, an analysis of the dose sufficiency signal will allow the test meter to record the percentage of fill of the capillary fill space for each measurement made by the test meter, if desired.

While the electrode geometry itself demonstrates an advantage over previous embodiments in terms of detecting an adequate sample, particularly in the case of a convex flow front, it was found that further improvement is achieved in the use of AC responses over DC responses for sample detection. DC responses have the problems of being sensitive to variations in, for example, temperature, hematocrit and the analyte (glucose for example). AC responses at sufficiently high frequency can be made robust to the variation in the analyte concentration. Further, the AC response generated at sufficiently high frequencies in such capillary fill devices is primarily limited by the amount of the parallel gap between the electrode edges which is filled by the sample. Thus, for a convex flow front, little or no AC response (in this case admittance) is perceived until the trough of the flow front actually intrudes within the parallel edges of the sample sufficiency electrodes. Further, by means of threshold calibration, the sensor can be made more or less sensitive as is deemed advantageous, with a higher threshold for admittance requiring more of the parallel gap to be filled before test initiation.

A further limitation of existing devices is the inability of the electrode geometry to discern the amount of time needed to fill the capillary space of the sensor. This limitation is caused by having interdependence of the dose sufficiency electrode and the measurement electrodes. This is a further advantage of independent dose sufficiency electrodes. In the preferred embodiment a signal is first applied across the measurement electrodes prior to dosing. When a response is observed, the potential is immediately switched off and a second signal is applied across the dose sufficiency electrodes during which time the system both looks for a response to the signal (indicating electrode coverage) and marks the duration between the first event (when a response is observed at the measurement electrodes) and the second event (when a response is observed at the dose sufficiency electrodes). In cases where very long intervals may lead to erroneous results, it is possible to establish a threshold within which acceptable results may be obtained and outside of which a failsafe is triggered, preventing a response or at a minimum warning the user of potential inaccuracy. The amount of time lag between dosing and detection of a sufficient sample that is considered allowable is dependent upon the particular sensor design and chemistry. Alternatively, an independent pair of dose detection electrodes (not shown) may be added upstream from the measurement electrodes in order to detect when the sample is first applied to the sensor.

While a DC signal could be used for detection in either or both of the above events, the preferred embodiment uses an AC signal at sufficiently high frequency to avoid unnecessarily perturbing the electrochemical response at the measurement electrodes and to provide robust detection with respect to flow front irregularities.

Control and Calibration Solutions

Certain embodiments of the control and calibration solutions according to the present disclosure contain an ionic modulator, an organic modulator or both. Ionic modulators are any substance having sufficient solubility in the solution to increase the ionic conductivity of the matrix by an amount sufficient to differentiate the control/calibration sample from a regular test sample. Inorganic and organic salts can both function as ionic modulators. Preferred ionic modulators include water soluble inorganic salts, such as sodium chloride, potassium chloride, calcium chloride, and the like. Ionic modulators generally have a large effect on the AC component of the response, but generally have very little effect on the DC component of the response. Organic modulators are any organic compound having sufficient solubility in the solution to decrease the ionic conductivity of the matrix sufficiently to differentiate the control/calibration sample from a regular test sample. Organic modulators typically decrease both the AC and DC components of the response of the matrix. Examples of organic modulators include, but are not limited to, water soluble, non-polymeric organic compounds such as propylene glycol, dipropylene glycol, ethylene glycol, glycerine, sorbitol and the like.

As described herein, the concentration of an analyte, such as glucose, can be determined from either AC or DC components of the responses. Once an AC or DC response component is chosen to determine the device's performance or the analyte concentration, any remaining response component is available for modification to identify whether the data generated is sample data or control/calibration data. For example, if the DC response component is chosen to reflect analyte concentration, an ionic modulator can be added to a control/calibration solution to cause the AC admittance (measured as a magnitude or a phase) to become uncharacteristically high. As a result, the data generated from the control/calibration solution can be identified as control/calibration data based on its AC response component. If an ionic modulator is added in sufficient quantity to unintentionally increase the DC response component, an organic modulator can be added as needed to reduce the DC response component to a desired value. By selecting and varying the relative amounts of ionic and organic modulators it is possible to “dial in” a desired uncharacteristic AC response component while maintaining a characteristic DC response component for a control/calibration solution. In a similar manner, the AC response component can be selected to reflect the amount of analyte present and the DC response component made uncharacteristically low by adding an organic modulator. As necessary, an ionic modulator can be selected and added in an amount sufficient to adjust the AC response component to a characteristic level. An uncharacteristically low DC response component for a control/calibration solution can be used to identify whether data generated is sample or control/calibration data. By constructing control/calibration solutions having designed AC and/or DC response components it is possible to utilize a single control/calibration solution for a variety of meters by simply setting different cut-off points to differentiate test data or by choosing different Matrix ID functions to differentiate test data from control/calibration data. Certain control and calibration solutions additionally contain a buffer such as HEPES, a preservative to control bacterial growth and optionally a coloring agent.

One Matrix ID function utilizing an AC response component is the arctangent of a binary equation involving temperature and admittance terms and an intercept term: MXID ₁=tan⁻¹ [m ₀ +m ₂ dT+m ₂(Y ₂ −Y ₁)]  (Equation 22)

The arctangent function drives the two data populations to different asymptotes and, with a properly selected intercept, provides data sets containing positive or negative numbers depending on whether the data was generated from actual test samples or control/calibration solutions. Intercept values can be chosen so that control/calibration solutions having an uncharacteristically high AC admittance will provide negative Matrix ID values whereas blood (or other analyte) samples will provide positive Matrix ID values. Similarly, intercepts can be selected so that solutions having an uncharacteristically low DC response will provide positive Matrix ID values compared to negative values for sample data.

Those skilled in the art will recognize that other functions can be substituted for the arctangent function. Also, the disclosed embodiments may utilize AC admittance measurements of magnitude and/or phase to identify data as being generated from a control/calibration solution.

A second Matrix ID function utilizes both AC admittance phase and magnitude responses and can be expressed in general form as: MXID=mx ₀ +mx ₁ P ₁ +mx ₂ P ₂ . . . mx _(n) P _(n) +mx _((n+1)) Y ₁ +mx _((n+2)) Y ₂ . . . +mx _(q) Y _(q)  (Equation 23) where m_(x) values are constants, P values are AC admittance phase measurements, and Y values are AC admittance magnitude measurements. The multiple P and Y terms correspond to a corresponding multiple of measurement frequencies. Terms corresponding to unused measurement frequencies can be removed from the equation by setting the corresponding constants to zero when the equation constants are input to the test meter, as will be appreciated by those skilled in the art. By selecting proper intercept (mx₀) and slope constants, the Matrix ID for control/calibration data can be made to always be greater than zero, whereas the Matrix ID for any test data can be made to always have a negative value (or vice versa).

As an example, a particular test apparatus may be configured to check for a control/calibration data after every test by applying the following Matrix ID equation to the measurement data: MXID=mx ₀ +mx ₁ P ₁ +mx ₂ P ₂ +mx ₃ P ₃ +mx ₄ P ₄ +mx ₅ P ₅ +mx ₆ P ₆ +mx ₇ Y ₁ +mx ₈ Y ₂ +mx ₉ Y ₃ +mx ₁₀ Y ₄ +mx ₁₁ Y ₅ +mx ₁₂ Y ₆  (Equation 23a) Equation 23a contains six possible admittance phase terms and six possible admittance magnitude terms because the test apparatus is capable of making test measurements at six different frequencies. Inclusion of any or all of these terms may be accomplished by supplying zero (non-inclusion) or non-zero (inclusion) constants to the meter for use in the MXID function during any particular test sequence. This may conveniently be done, for example, by supplying the constants to the test apparatus using a code key supplied with the test strips or by encoding information readable by the test strip directly onto the test strip being used for the test, as is known in the art.

For example, if the test sample data and control/calibration data populations may be separated using only admittance phase test data taken at 20 kHz, and the mx₃P₃ term is associated with the 20 kHz admittance phase data, all constants except mx₀ and mx₃ in the MXID function can be set to zero (mx₀ can also be set to zero if that results in the desired intercept value). In one embodiment of test strip reagent chemistries and control/calibration solution compositions, these values can be selected such that MXID >0 indicates the test data is control/calibration data.

Suppose, however, that the test apparatus also works with a second type of test strip having a different reagent chemistry, and use of these test strips does not result in adequately separated data populations between test sample data and control/calibration data when using only the 20 kHz admittance phase data and the original control solution. In such a case, it may be determined that including the admittance phase data at 10 kHz and 20 kHz, while including the admittance magnitude data at 1 kHz and 5 kHz will yield a MXID function result that has appropriately separated result populations for sample data and control/calibration data when using the original control solution. By providing a flexible MXID function where terms can be selected by supplying various constants from a data source (e.g. code key or on-strip encoding, just to name two non-limiting examples), the test meter can be configured to segregate the data populations appropriately without the need to provide a different control solution for each type of test strip.

A third example of Matrix ID relies on the different populations of Normalized Cottrell Failsafe Ratios (NCFR) generated by control/calibration solutions and test samples. As discussed hereinabove with respect to equation 17, the Normalized Cottrell Failsafe Ratio can be defined as:

$\begin{matrix} {{N\; C\; F\; R} = {\frac{\sum\limits_{k = 1}^{m}I_{k}}{{mI}_{m}} = {\frac{\sum\limits_{k = 1}^{m}{\frac{{nFA}\sqrt{D}}{\sqrt{\Pi}}{Ct}_{k}^{\alpha}}}{m\frac{{nFA}\sqrt{D}}{\sqrt{\Pi}}{Ct}_{m}^{\alpha}} = {\frac{\sum\limits_{k = 1}^{m}t_{k}^{\alpha}}{{mt}_{m}^{\alpha}} = {Constant}}}}} & \left( {{Equation}\mspace{14mu} 17} \right) \end{matrix}$ A plot of the NCFR versus temperature for control/calibration solutions and test samples can provide two separated data populations, as illustrated in FIG. 43. Because a range of separation exists between the two data populations, the identification of the test data as a control/calibration response can be based upon whether the NCFR at a particular temperature is more than a predetermined magnitude or a Matrix ID function may be derived to cause control/calibration data to be greater than zero and test data to be a negative number. One Matrix ID function relying on an uncharacteristic Normalized Cottrell Failsafe Ratio includes:

$\begin{matrix} {{MXID} = {\tan^{- 1}\left\lbrack {m_{0} + {m_{1}{dT}} + {m_{2}{\sum\limits_{k = 1}^{m}{I_{k}/{Im}}}}} \right\rbrack}} & \left( {{Equation}\mspace{14mu} 24} \right) \end{matrix}$ where: MXID is the matrix ID, m₀, m₁, and m₂ are constants, dT is the temperature value, I_(k) is the Cottrell current at time k, and I_(m) is the Cottrell current at a subsequent time m.

Application of a Matrix ID function to control/calibration data and test data facilitates differentiation of control/calibration data from normal test data by the test meter. Such differentiation is particularly important for test meters that record and retain test data for a specified number of determinations for later review by an individual or an individual's physician. Co-mingling of undifferentiated control/calibration data with normal test data would reduce the value of such retained data. Because a test meter utilizing a Matrix ID function can automatically recognize control/calibration data, user error resulting in data contamination, such as for example saving control/calibration data as test data, is avoided. Furthermore, the ability to record control/calibration data separately provides a separate record of the test meter's performance and accuracy for a determined period of time and can be useful in interpreting the normal test data and monitoring the meter's performance. Finally, the use of Matrix ID functions allows a single control/calibration solution coupled with different Matrix ID functions to be used in a variety of devices that utilize different chemistry. As a result, a single control/calibration can be developed to function with a variety of devices equipped with proper Matrix ID functions. By way of example only and not of limitation, the solutions disclosed herein and their use allows a test meter to receive samples of solutions and test fluids, generate corresponding data, recognize the data's identity and automatically segregate control/calibration data from normal test data.

Control solutions having a known uncharacteristic admittance allow the test meter to recognize that a performance check is underway and treat the control data in a prescribed manner. For example, control data might be stored in the device in a file designed to contain control data or the control data may be stored with other non-control data by using a flag to identify the control data. Upon identification of the control data, the meter might perform a self-diagnostic adjustment as indicated by the control data generated. If the self-adjustment is insufficient to bring the meter within its specifications, a notice to have the meter serviced can be provided. Other options are also possible. Comparison of the measured DC response with the known value can provide a measure of the meter's performance. Calibration solutions generally have a known concentration of an analyte ranging from zero to an upper limit determined by the upper level of analyte normally measured by the meter. The solution's uncharacteristic admittance enables the test meter to recognize that an accuracy check is underway and treat the calibration data in a prescribed manner. Comparison of the measured analyte concentration with the known analyte concentration provides a measure of accuracy. If the meter's reading for analyte is outside of a preset limit based on the known concentration of analyte, an adjustment or calibration of the meter might be carried out. If calibration fails to bring the meter within its specifications, notice can be provided to have the meter serviced. Other options are also possible.

Certain methods employing the control and calibration solutions described above involve applying a signal to the solution having an AC and/or DC component and measuring at least one response generated by the solution. For some methods the AC signal component has a frequency of from about 1 Hz to about 20 kHz. For some methods, the response is an admittance for which a magnitude or phase is determined. Certain methods employing calibration solutions additionally comprise determining the concentration of the analyte component of the solution from a characteristic response obtained utilizing methods known in the art and those methods disclosed herein.

Although Examples 9-11 utilize a particular biological fluid test strip and methods to determine the glucose level for calibration purposes, one skilled in the art will recognize that calibration according to the present disclosure can be carried out with different test strips and utilizing a variety of methods for determining the glucose level as well as the level of other analytes.

EXAMPLE 9 Control and Calibration Solutions Identified with a Matrix ID Function Based on Admittance Magnitude

Generally, control solutions and calibration solutions are compositions in the form of a solution, which can be used to measure the performance or the accuracy of a device. A control solution can function as a calibration solution having no analyte. Calibration solutions can be readily formed by adding a known amount of analyte to a known quantity of a control solution.

The composition of a first embodiment of a control solution according to the present disclosure is detailed in Table VII and the composition of a first embodiment of a calibration solution derived from the first embodiment control solution is detailed in Table VIII.

TABLE VII Control Solution (bulk) Component Quantity Propylene Glycol 282.200 g HEPES acid* 40.122 g Sodium HEPES 8.234 g Sodium Chloride 31.815 g Calcium Chloride (dihydrate) 0.000 g Germall ® II Preservative** (Diazolidinyl Urea) 3.000 g FD&C; Blue #1 (12% dye solution) 0.300 g Reverse Osmosis DI Water 634.329 g Total 1000.0 g *HEPES is N-(2-hydroxyethyl)-piperazine-N′-2-ethanesulfonic acid **Germall is a registered trademark of Sutton Laboratories, Inc., 459 E. First Ave, Roselle, New Jersey 07203.

TABLE VIII Calibration Solution Calibration Solution Glucose/100 g Bulk Solution Level 1 0.071 g Level 2 0.103 g Level 3 0.234 g Level 4 0.429 g Level 5 0.690 g Level 6 0.756 g A minimal amount of the supporting electrolyte is needed for control and calibration solutions. For embodiments studied, the necessary amount is at least about 10 mM for each 1000 g of solution. Use of the first control solution provides an uncharacteristic admittance reading that can be used to identify the data as control data and a DC response that provides a measure of the device's performance. Similarly, use of the first calibration solution provides a measured glucose level that can be compared to the solution's known glucose level. The control and calibration data generated with these solutions can be distinguished from normal test data either by identifying a threshold level above or below which data is identified as control/calibration data or by using a Matrix ID function of the types illustrated herein. Data recognized as control/calibration data can be processed according to protocols determined for the meter that avoid co-mingling control/calibration data with normal test data.

For the purposes of demonstrating the utility of the present disclosure in distinguishing control/calibration data from test data, additional tests using the first embodiment control solution described above were performed along side the tests described hereinabove with respect to Example 5, using test strip 1700.

FIG. 37 illustrates the admittances of each blood sample and each calibration solution measured at 20 kHz and plotted against temperature. The data plotted shows a pattern of separation between the admittance of blood samples and calibration solutions. Based on this separation, for each temperature, a threshold limit can be set at a particular admittance identifying any admittance below the designated threshold as corresponding to a blood sample and any admittance above the designated threshold as corresponding to a calibration solution. However, such a threshold would have to be set for each temperature at which measurements are taken.

Because we know from FIG. 37 that admittance is linearly related to temperature we can define the Matrix ID function (MXID) as follows: MXID ₁=tan⁻¹ [m ₀ +m ₂ dT+m ₂(Y ₂ −Y ₁)]  (Equation 22) where m₀, m₁, and m₂ are constants, dT is the temperature value defined as the difference between the meter reported temperature and a “nominal” temperature (in this Example 24° C.), and Y is the admittance determined at frequencies 1 and 2. The arctangent function was chosen to drive the two data populations to different asymptotes and the intercept term m₀ was included so that samples displaying a Matrix ID of less than zero can be identified as control/calibration solutions whereas samples having a Matrix ID greater than zero can be identified as blood samples.

The Matrix ID functions (Equation 22) for control solution samples and for blood samples based on admittances obtained at 10 kHz and 1 kHz were determined and plotted against temperature and are illustrated in FIG. 38. As can be seen, the Matrix ID for blood samples having hematocrit levels ranging from 20% to 70% and tested at each of five temperatures provided a consistently positive value, whereas the Matrix ID for control solutions provided a consistently negative value. The Matrix ID for calibration samples similarly provides a consistently negative value. A test meter provided with a protocol for determining the Matrix ID and handling the data based on a sample's Matrix ID can, without further input, distinguish whether a test initiated is a normal test or a control or calibration determination and segregate control and/or calibration data from test data accordingly. Such data segregation is particularly useful for test meters that store data for future review by an individual or the individual's physician. The development of a specific and appropriate meter protocol can readily be carried out by one of ordinary skill in the art.

EXAMPLE 10 Control and Calibration Solutions Identified with a Matrix ID Function Based on Admittance Magnitude and Phase

A second embodiment of a control solution according to the present disclosure is detailed in Table IX. Further embodiments of calibration solutions are detailed in Table X.

TABLE IX Calibration Solution Component Concentration Quantity Propylene Glycol 10.00%  100.000 g HEPES acid* 168.4 mM 40.122 g Sodium HEPES  31.6 mM 8.234 g Sodium Chloride 568.4 mM 33.215 g Calcium Chloride (dihydrate)  4.5 mM 0.662 g Germall II 0.30% 3.000 g FD&C; Blue #1 (13% dye solution) 0.59% 5.900 g Reverse Osmosis DI water 80.9% 808.900 g Total  100% 1000.033 g *HEPES is N-(2-hydroxyethyl)-piperazine-N′-2-ethanesulfonic acid **Germall is a registered trademark of Sutton Laboratories, Inc., 459 E. First Ave, Roselle, New Jersey 07203.

TABLE X Calibration Solution Calibration Solution Glucose/100 g Bulk Solution Level 1 0.071 g Level 2 0.103 g Level 3 0.234 g Level 4 0.429 g Level 5 0.690 g Level 6 0.756 g

Samples of blood having 20%, 31%, 42%, 53%, and 64% hematocrit and the control sample from Table IX were analyzed with an ACCU-CHEK® Aviva glucose meter utilizing a glucose dehydrogenase reagent. FIG. 39 illustrates the phase angle measured at 20 kHz plotted against temperature. By relying on one phase angle (P3), the control sample could be distinguished and the test meter instructed to recognize any data associated with a 20 kHz phase angle of more than about 27 as being control. The calibration samples from Table X can likewise be tested and the calibration data also distinguished from test data. Similarly, the test meter can be programmed to recognize any data associated with a 20 kHz phase angle of less than about 27 as normal test data.

Samples of blood having 20%, 31%, 42%, 56%, and 70% hematocrit and the control sample from Table IX were analyzed with an ACCU-CHEK® Aviva glucose meter utilizing a glucose oxidase reagent. FIG. 40 illustrates the 20 kHz admittance plotted against temperature. By relying on 20 kHz admittance magnitude, a control/calibration sample can be distinguished and the test meter instructed to recognize any data associated with a 20 kHz admittance of more than about 1600 as being control or calibration data. Similarly, the test meter can be programmed to recognize any data associated with a 20 kHz admittance of less than about 1600 as normal test data.

The Matrix ID function provided in Equation 23a can also be utilized to facilitate the identification of control/calibration data. MXID=mx ₀ +mx ₁ P ₁ +mx ₂ P ₂ +mx ₃ P ₃ +mx ₄ P ₄ +mx ₅ P ₅ +mx ₆ P ₆ +mx ₇ Y ₁ +mx ₈ Y ₂ +mx ₉ Y ₃ +mx ₁₀ Y ₄ +mx ₁₁ Y ₅ +mx ₁₂ Y ₆  (Equation 23a) where “m×” values are constants, P represents an admittance phase measurement and Y represents an admittance magnitude. Values of mx can be selected to cause individual components of Equation 23a to equal zero, thus causing the Matrix ID to depend on one response or a combination of responses. With a properly chosen intercept, mx₀, a Matrix ID response greater than zero will identify associated data as related to a control/calibration measurement.

Samples of blood having 20%, 31%, 42%, 56%, and 70% hematocrit and the control sample from Table IX were analyzed with an ACCU-CHEK® Aviva glucose meter utilizing a glucose oxidase reagent. FIG. 41 illustrates the MXID plotted against temperature. As can be seen from examination of FIG. 41, all control samples provide a MXID that is greater than zero, whereas all blood samples provide a MXID of less than zero. Analyte concentration for a calibration or blood sample can be determined from the DC response. By relying on the MXID function, control/calibration data can be distinguished from test data and the test meter instructed to store each type of data in the appropriate file.

ACCU-CHEK is a registered U.S. trademark of Roche Diagnostics GmbH CORPORATION FED REP GERMANY, Sandhofer Strasse, 116 Mannheim FED REP GERMANY D-68305.

EXAMPLE 11 Control and Calibration Solutions Identified with a Matrix ID Function Based on the Cottrell Failsafe Ratio

In some instances it may be desirable to utilize the AC response to determine analyte concentration in blood samples and calibration samples and thus utilize the DC response to identify control/calibration data. A control/calibration solution can be prepared by adding a sufficient quantity of an organic modulator, such as dipropylene glycol, to increase the DC response to an uncharacteristically low level. Because organic modulators similarly decrease the AC response, an appropriate amount of an inorganic modulator such as sodium chloride can be added to bring the AC response back to a characteristic response. One skilled in the relevant art would be able to “dial in” this characteristic AC response while maintaining the uncharacteristic DC response for any reagent chemistry without undue experimentation.

FIG. 42 illustrates typical DC responses obtained for blood samples and control/calibration samples having an uncharacteristic DC response. One convenient way to identify a control/calibration sample relies on the Normalized Cottrell Failsafe Ratio defined in Equation 17. FIG. 43 illustrates a plot of the Normalized Cottrell Failsafe Ratio plotted against temperature. As can be seen from examination of FIG. 43, a test meter can be programmed to recognize any data associated with a Cottrell Failsafe Ratio of less than the determined number “a” as control/calibration data. Similarly, any data associated with a Cottrell Failsafe Ratio of more than the determined number can be recognized by the test meter as test data.

As shown in the previous examples, a MXID function can be developed to facilitate recognition of control/calibration data by a test meter. Equation 24 illustrates one particularly appropriate MXID function associated with the Cottrell Failsafe Ratio. FIG. 44 illustrates MXID values determined from Equation 24 plotted against temperature. As can be seen with reference to FIG. 42, any data associated with a MXID value of less than zero is control/calibration data, whereas any data having a MXID value of more than zero is sample data.

All publications, prior applications, and other documents cited herein are hereby incorporated by reference in their entirety as if each had been individually incorporated by reference and fully set forth.

While the invention has been illustrated and described in detail in the drawings and foregoing description, the description is to be considered as illustrative and not restrictive in character. Only the preferred embodiment, and certain other embodiments deemed helpful in further explaining how to make or use the preferred embodiment, have been shown. All changes and modifications that come within the spirit of the invention are desired to be protected. 

1. A method for identifying control/calibration data generated by a medical device, the method comprising the steps of: (a) providing a control/calibration solution containing at least one analyte and containing a sufficient amount of a modulator to cause the solution to provide two electrochemical responses to an applied signal, wherein one electrochemical response is characteristic of blood and one electrochemical response is uncharacteristic of blood wherein said modulator is selected from the group consisting of an ionic modulator, and a combination of an ionic modulator and an organic modulator; (b) applying a signal containing AC and DC components to the control/calibration solution; (c) measuring the two electrochemical responses; (d) using the characteristic electrochemical response to provide control/calibration data; and (e) using the uncharacteristic electrochemical response to identify control/calibration data.
 2. The method of claim 1, wherein using the characteristic electrochemical response involves providing control data.
 3. The method of claim 1, wherein using the characteristic electrochemical response involves providing calibration data.
 4. The method of claim 1, wherein applying a signal involves applying a signal containing an AC component having a frequency of between about 1 Hz and about 20 kHz.
 5. The method of claim 1, wherein the uncharacteristic electrochemical response is admittance.
 6. The method of claim 5, wherein measuring the electrochemical responses involves measuring an uncharacteristic electrochemical response comprising admittance magnitude information.
 7. The method of claim 5, wherein measuring the electrochemical responses involves measuring an uncharacteristic electrochemical response comprising admittance phase information.
 8. The method of claim 5, wherein step (e) comprises determining a Matrix ID using the equation: MXID=tan⁻¹ [m ₀ +m ₁ dT+m ₂(Y ₂ −Y ₁)] where: MXID is the matrix ID, m₀, m₁, and m₂ are constants, dT is the temperature value, and Y is the admittance determined at frequencies 1 and
 2. 9. The method of claim 8, wherein applying a signal involves applying a signal having a frequency of between about 1 Hz and about 20 kHz.
 10. The method of claim 5, wherein step (e) comprises determining a Matrix ID using the equation: MXID=mx ₀ +mx ₁ P ₁ +mx ₂ P ₂ +mx ₃ P ₃ +mx ₄ P ₄ +mx ₅ P ₅ +mx ₆ P ₆ +mx ₇ Y ₁ +mx ₈ Y ₂ +mx ₉ Y ₃ +mx ₁₀ Y ₄ +mx ₁₁ Y ₅ +mx ₁₂ Y ₆ where: MXID is the matrix ID, mx₁₋₁₂ are constants, P₁₋₆ are the phases of the admittances for selected frequencies Y₁₋₆ are the magnitude of the admittances for the same frequencies.
 11. The method of claim 10, wherein applying a signal involves applying a signal having a frequency of between about 1 Hz and about 20 kHz.
 12. The method of claim 1, wherein providing a control/calibration solution involves providing a solution containing an organic modulator, applying a signal involves applying a signal including a DC component, measuring an uncharacteristic electrochemical response involves measuring a current, and step (e) comprises determining a Matrix ID using the equation: $\begin{matrix} {{MXID} = {\tan^{- 1}\left\lbrack {m_{0} + {m_{1}{dT}} + {m_{2}{\sum\limits_{k = 1}^{m}{I_{k}/{Im}}}}} \right\rbrack}} & \; \end{matrix}$ where: MXID is the matrix ID, m₀, m₁, and m₂ are constants, dT is the temperature value, I_(k) is the Cottrell current at time k, and I_(m) is the Cottrell current at a subsequent time m.
 13. A method for identifying control/calibration data generated by a device having a test chamber and designed to analyze blood, the method comprising: (a) selecting a control/calibration solution containing at least one analyte and containing a modulator selected from the group consisting of an ionic modulator, and a combination of an ionic modulator and an organic modulator, wherein the selecting includes selecting an amount of said modulator sufficient to cause the solution to provide two electrochemical responses, wherein one electrochemical response is characteristic of blood and one electrochemical response is uncharacteristic of blood; (b) introducing the solution into the test chamber; (c) applying a signal including an AC component to the solution; (d) generating and measuring an uncharacteristic electrochemical response comprising an admittance; and (e) using the uncharacteristic electrochemical response to identify control/calibration data.
 14. The method of claim 13, additionally generating and measuring a characteristic response and using the characteristic response to provide control data.
 15. The method of claim 13, additionally generating and measuring a characteristic electrochemical response and using the characteristic electrochemical response to provide calibration data.
 16. The method of claim 15, wherein using the characteristic electrochemical response to provide calibration data involves providing data relating to the concentration of an analyte.
 17. The method of claim 16, wherein the device is a glucose test meter and using the characteristic electrochemical response to provide the concentration of an analyte involves providing the concentration of glucose.
 18. The method of claim 17, wherein applying the signal involves applying a signal having a frequency of between about 1 Hz and about 20 kHz.
 19. The method of claim 13, wherein step (e) comprises determining the Matrix ID using the equation: MXID=tan⁻¹ [m ₀ +m ₁ dT+m ₂(Y ₂ −Y ₁)] where: MXID is the matrix ID, m₀, m₁, and m₂ are constants, dT is the temperature value, and Y is the admittance determined at frequencies 1 and
 2. 20. The method of claim 13, wherein step (d) comprises determining a Matrix ID using the equation: MXID=mx ₀ +mx ₁ P ₁ +mx ₂ P ₂ +mx ₃ P ₃ +mx ₄ P ₄ +mx ₅ P ₅ +mx ₆ P ₆ +mx ₇ Y ₁ +mx ₈ Y ₂ +mx ₉ Y ₃ +mx ₁₀ Y ₄ +mx ₁₁ Y ₅ +mx ₁₂ Y ₆ where: MXID is the matrix ID, mx₁₋₁₂ are constants, P₁₋₆ are the phases of the admittances for selected frequencies Y₁₋₆ are the magnitude of the admittances for the same frequencies.
 21. The method of claim 13, wherein applying the signal involves applying a signal including a DC component.
 22. The method of claim 21, wherein step (e) comprises determining a Matrix ID using the equation: ${MXID} = {\tan^{- 1}\left\lbrack {m_{0} + {m_{1}{dT}} + {m_{2}{\sum\limits_{k = 1}^{m}{I_{k}/{Im}}}}} \right\rbrack}$ where: MXID is the matrix ID, m₀, m₁, and m₂ are constants, dT is the temperature value, I_(k) is the Cottrell current at time k, and I_(m) is the Cottrell current at a subsequent time m.
 23. A method for generating and identifying control/calibration data generated by a device designed to analyze blood, the method comprising: (a) providing a test strip; (b) providing a control/calibration solution containing at least one analyte and containing a known concentration of analyte and a modulator selected from the group consisting of an ionic modulator, and a combination of an ionic modulator and an organic modulator, wherein the providing includes providing an amount of the moderator sufficient to cause the solution to provide two electrochemical responses, wherein one electrochemical response is characteristic of blood and one electrochemical response is uncharacteristic of blood; (c) applying the solution to the test strip; (d) applying test and control/calibration signals to the solution, wherein said control/calibration signal has an AC component; (e) measuring the characteristic electrochemical response to the test signal; (f) using the characteristic electrochemical response to determine the analyte concentration; (g) measuring the uncharacteristic electrochemical response to the control/calibration signal, wherein said measuring involves measuring admittance; and (h) using the uncharacteristic electrochemical response to identify the analyte concentration as control/calibration data.
 24. The method of claim 23, wherein applying the control/calibration signal involves applying a signal having an AC component having a frequency of from about 1 Hz to about 20 kHz.
 25. The method of claim 24, wherein step (h) comprises determining the Matrix ID using the equation: MXID=tan⁻ [m ₀ +m ₁ dT+m ₂(Y ₂ −Y ₁)] where: MXID is the matrix ID, m₀, m₁, and m₂ are constants, dT is the temperature value, and Y is the admittance determined at frequencies 1 and
 2. 26. The method of claim 24, wherein step (h) comprises determining a Matrix ID using the equation: MXID=mx ₀ +mx ₁ P ₁ +mx ₂ P ₂ +mx ₃ P ₃ +mx ₄ P ₄ +mx ₅ P ₅ +mx ₆ P ₆ +mx ₇ Y ₁ +mx ₈ Y ₂ +mx ₉ Y ₃ +mx ₁₀ Y ₄ +mx ₁₁ Y ₅ +mx ₁₂ Y ₆ where: mx₁₋₁₂ are constants, P₁₋₆ are the phases of the admittances for selected frequencies Y₁₋₆ are the magnitude of the admittances for the same frequencies.
 27. The method of claim 23, wherein applying a control/calibration signal involves applying a signal having a DC component.
 28. The method of claim 27, wherein step (h) comprises determining a Matrix ID using the equation: ${MXID} = {\tan^{- 1}\left\lbrack {m_{0} + {m_{1}{dT}} + {m_{2}{\sum\limits_{k = 1}^{m}{I_{k}/{Im}}}}} \right\rbrack}$ where: MXID is the matrix ID, m₀, m₁, and m₂ are constants, dT is the temperature value, I_(k) is the Cottrell current at time k, and I_(m) is the Cottrell current at a subsequent time m. 